Maths-
General
Easy

Question

I f space u equals tan to the power of negative 1 space end exponent open parentheses fraction numerator x cubed plus y cubed over denominator x minus y end fraction close parentheses space t h e n space x squared fraction numerator partial differential squared u over denominator partial differential x squared end fraction plus 2 x y fraction numerator partial differential squared u over denominator partial differential x partial differential y end fraction plus y squared fraction numerator partial differential squared u over denominator partial differential y squared end fraction equals

  1. open parentheses 2 space C o s 2 u minus 1 close parentheses space S i n space 2 u space
  2. left parenthesis 2 space Cos space space 2 u plus 1 right parenthesis Sin space 2 u
  3. left parenthesis Sin space 2 u minus 1 right parenthesis Cos space 2 u
  4. left parenthesis Sin space 2 u plus 1 right parenthesis Cos space 2 u

hintHint:

We are given the value of u. We have to find the value of the equation for given value of u. We will first find the degree of the equation. Then, we will solve the given equation.

The correct answer is: open parentheses 2 space C o s 2 u minus 1 close parentheses space S i n space 2 u space


    The given value of u is as follows:
    u equals tan to the power of negative 1 end exponent open parentheses fraction numerator x cubed plus y cubed over denominator x minus y end fraction close parentheses
    We have to find the value of
    x squared fraction numerator partial differential squared u over denominator partial differential x squared end fraction plus 2 x y fraction numerator partial differential squared u over denominator partial differential x partial differential y end fraction plus y squared fraction numerator partial differential squared u over denominator partial differential y squared end fraction space equals space ?
    We will simplify u before solving it further.
    Let  z = tanu
    Here, z = f(u)
    So,
    table attributes columnalign left end attributes row cell z equals fraction numerator x cubed plus y cubed over denominator x minus y end fraction end cell row cell space space equals fraction numerator x cubed open parentheses 1 space plus space begin display style y cubed over x cubed end style close parentheses over denominator x open parentheses 1 space minus begin display style y over x end style close parentheses end fraction end cell row cell space space equals x squared fraction numerator 1 space plus space begin display style y cubed over x cubed end style over denominator 1 space minus begin display style y over x end style end fraction end cell row cell space space space space space equals x squared f open parentheses y over x close parentheses end cell end table
    The degree of function is 2.
    When z = f(u)
    x squared fraction numerator partial differential squared u over denominator partial differential x squared end fraction plus 2 x y fraction numerator partial differential squared u over denominator partial differential x partial differential y end fraction plus y squared fraction numerator partial differential squared u over denominator partial differential y squared end fraction equals g left parenthesis u right parenthesis left square bracket g apostrophe left parenthesis u right parenthesis space minus 1 right square bracket
H e r e comma
space space space space space space space space g left parenthesis u right parenthesis equals n fraction numerator f left parenthesis u right parenthesis over denominator f apostrophe left parenthesis u right parenthesis end fraction

F o r space t h e space g i v e n space e q u a t i o n

space space space space space space space space space space f left parenthesis u right parenthesis equals tan u

S o comma space f apostrophe left parenthesis u right parenthesis equals s e c squared u
    g left parenthesis u right parenthesis equals 2 fraction numerator tan u over denominator s e c squared u end fraction space
space space space space space space space space space equals 2 fraction numerator begin display style fraction numerator sin u over denominator cos u end fraction end style over denominator begin display style fraction numerator 1 over denominator cos squared u end fraction end style end fraction
space space space space space space space space space equals 2 sin u cos u
space space g left parenthesis u right parenthesis equals sin 2 u
    g'(u) = 2cos2u
    The solution will be
    x squared fraction numerator partial differential squared u over denominator partial differential x squared end fraction plus 2 x y fraction numerator partial differential squared u over denominator partial differential x partial differential y end fraction plus y squared fraction numerator partial differential x over denominator partial differential y squared end fraction equals sin 2 u left parenthesis 2 cos 2 u space minus space 1 right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space
    The option which is "(2cos2u - 1)sin2u", is the right option.

    We need to remember different formulas for this type of questions.

    Related Questions to study

    General
    physics-

    Two masses M and M/2 are joincd togcther by means of light inexcusable string passed aver z, fictiodess pullcy as shown in fig. Whcn the bigger mass is rekasod, the small ane will ascend with an acceleration

    Two masses M and M/2 are joincd togcther by means of light inexcusable string passed aver z, fictiodess pullcy as shown in fig. Whcn the bigger mass is rekasod, the small ane will ascend with an acceleration

    physics-General
    General
    physics-

    A particle of mass 2 text end text k g is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below,The velocity of the particle after 10 s is

    A particle of mass 2 text end text k g is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below,The velocity of the particle after 10 s is

    physics-General
    General
    physics-

    A solid sphere of mass 2 text end text k g is resting inside a cube as shown in the figure. The cube is moving with a velocity stack v with rightwards arrow on top equals left parenthesis 5 t i plus 2 t stack j with hat on top right square bracket right parenthesis m s to the power of negative 1 end exponent Here t is the time in scond. All surfaces are smooth. The sphene is at rest with respect to the cube. what is the total force exerted by the sphene on the cube (g=10ms-2) )

    A solid sphere of mass 2 text end text k g is resting inside a cube as shown in the figure. The cube is moving with a velocity stack v with rightwards arrow on top equals left parenthesis 5 t i plus 2 t stack j with hat on top right square bracket right parenthesis m s to the power of negative 1 end exponent Here t is the time in scond. All surfaces are smooth. The sphene is at rest with respect to the cube. what is the total force exerted by the sphene on the cube (g=10ms-2) )

    physics-General
    parallel
    General
    chemistry-

    Oxygen has an oxidation state of +2 in the compound

    Oxygen has an oxidation state of +2 in the compound

    chemistry-General
    General
    physics-

    Three Forces F subscript 1 end subscript text end text F subscript 2 end subscript and F subscript 1 end subscript together kccp a body in equilhcium. If F subscript 1 end subscript equals 3 text end text N along the positive X text end text text .axis end text blank F subscript 2 end subscript equals 4 text end text N along the positive Y. axis, then the third force F subscript 3 end subscript is

    Three Forces F subscript 1 end subscript text end text F subscript 2 end subscript and F subscript 1 end subscript together kccp a body in equilhcium. If F subscript 1 end subscript equals 3 text end text N along the positive X text end text text .axis end text blank F subscript 2 end subscript equals 4 text end text N along the positive Y. axis, then the third force F subscript 3 end subscript is

    physics-General
    General
    physics-

    The Figure shows the Position-time (x-1) graph of one dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is

    The Figure shows the Position-time (x-1) graph of one dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is

    physics-General
    parallel
    General
    chemistry-

    In the reaction, 2FeSO4 + H2SO4 + H2O2 ® Fe2 (SO4)3 + 2H2O) the oxidizing agent is

    In the reaction, 2FeSO4 + H2SO4 + H2O2 ® Fe2 (SO4)3 + 2H2O) the oxidizing agent is

    chemistry-General
    General
    physics-

    A lift is going up. The total mass of the lift and the passenger is 1000 kg The variation in the speed of the lift is as given in the graph. The tension in the rope pulling the lift at t= 10.5sec will be

    A lift is going up. The total mass of the lift and the passenger is 1000 kg The variation in the speed of the lift is as given in the graph. The tension in the rope pulling the lift at t= 10.5sec will be

    physics-General
    General
    Maths-

    If u equals f left parenthesis x comma y right parenthesis is a homogeneous function of order n.

    I) x fraction numerator straight partial differential u over denominator straight partial differential x end fraction plus y fraction numerator straight partial differential u over denominator straight partial differential y end fraction equals n u

    II) x squared fraction numerator straight partial differential squared u over denominator straight partial differential x squared end fraction plus 2 x y fraction numerator straight partial differential squared u over denominator straight partial differential x straight partial differential y end fraction plus y squared fraction numerator straight partial differential squared u over denominator straight partial differential y squared end fraction equals n left parenthesis n minus 2 right parenthesis u

    III) x fraction numerator straight partial differential squared u over denominator straight partial differential x squared end fraction plus y fraction numerator straight partial differential squared u over denominator straight partial differential x straight partial differential y end fraction equals left parenthesis n minus 1 right parenthesis fraction numerator straight partial differential u over denominator straight partial differential x end fraction

    Which of the above statements is correct ?

    We have to remember all the three results instead of deriving them.

    If u equals f left parenthesis x comma y right parenthesis is a homogeneous function of order n.

    I) x fraction numerator straight partial differential u over denominator straight partial differential x end fraction plus y fraction numerator straight partial differential u over denominator straight partial differential y end fraction equals n u

    II) x squared fraction numerator straight partial differential squared u over denominator straight partial differential x squared end fraction plus 2 x y fraction numerator straight partial differential squared u over denominator straight partial differential x straight partial differential y end fraction plus y squared fraction numerator straight partial differential squared u over denominator straight partial differential y squared end fraction equals n left parenthesis n minus 2 right parenthesis u

    III) x fraction numerator straight partial differential squared u over denominator straight partial differential x squared end fraction plus y fraction numerator straight partial differential squared u over denominator straight partial differential x straight partial differential y end fraction equals left parenthesis n minus 1 right parenthesis fraction numerator straight partial differential u over denominator straight partial differential x end fraction

    Which of the above statements is correct ?

    Maths-General

    We have to remember all the three results instead of deriving them.

    parallel
    General
    physics

    Rockets are launched in eastward direction to take advantage of

    Rockets are launched in eastward direction to take advantage of

    physicsGeneral
    General
    physics

    The  additional K.E. to be provided to a satellite of mass m revolving around a planet of mass M , to transfer it from a circular orbit of radius R1 to another radius R2(R2>R1) is

    The  additional K.E. to be provided to a satellite of mass m revolving around a planet of mass M , to transfer it from a circular orbit of radius R1 to another radius R2(R2>R1) is

    physicsGeneral
    General
    chemistry-

    A reduction in atomic size with increase in atomic number is a characteristic of elements of

    A reduction in atomic size with increase in atomic number is a characteristic of elements of

    chemistry-General
    parallel
    General
    physics

    A satellite moves in a circle around the earth, the radius of this circle is equal to one half of the radius of the moon's orbit the satellite completes one revolution in

    A satellite moves in a circle around the earth, the radius of this circle is equal to one half of the radius of the moon's orbit the satellite completes one revolution in

    physicsGeneral
    General
    physics

    Two satellites A and B go round a planet in circular orbits having rarely 4 R and  If the speed of satellite A is 3V, then speed of satellite B is

    Two satellites A and B go round a planet in circular orbits having rarely 4 R and  If the speed of satellite A is 3V, then speed of satellite B is

    physicsGeneral
    General
    chemistry-

    The yellow coloured solution of salt of chromate ions change to orange colour on acidification due to the formation of

    The yellow coloured solution of salt of chromate ions change to orange colour on acidification due to the formation of

    chemistry-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.