Maths-
General
Easy

Question

fraction numerator d over denominator d x end fraction open parentheses Tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator a minus x over denominator 1 plus infinity x end fraction close parentheses close parentheses equals

  1. fraction numerator negative 1 over denominator 1 plus x to the power of 2 end exponent end fraction    
  2. fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction    
  3. fraction numerator a over denominator 1 plus x to the power of 2 end exponent end fraction    
  4. fraction numerator negative a over denominator 1 plus x to the power of 2 end exponent end fraction    

hintHint:

We are given a function. We have to find it's derivative. We will simplify the given function and find derivative.

The correct answer is: fraction numerator negative 1 over denominator 1 plus x to the power of 2 end exponent end fraction


    The given function fraction numerator d over denominator d x end fraction open curly brackets tan to the power of negative 1 end exponent space open parentheses fraction numerator a space minus space x over denominator 1 space plus space a x end fraction close parentheses close curly brackets

    W e space w i l l space u s e space t h e space f o r m u l a space t o space s o l v e space t h e space q u e s t i o n
tan to the power of negative 1 end exponent open parentheses fraction numerator p space minus space q over denominator 1 space plus space p q end fraction close parentheses space equals space tan to the power of negative 1 end exponent left parenthesis p right parenthesis space minus space tan to the power of negative 1 end exponent left parenthesis q right parenthesis
space p space a n d space q space c a n space b e space v a r i a b l e space o r space c o n s tan t s

    We will take the given function and simplify it first.
    tan to the power of negative 1 end exponent open parentheses fraction numerator a space minus space x over denominator 1 space plus space a x end fraction close parentheses space equals space tan to the power of negative 1 end exponent left parenthesis a right parenthesis space minus space tan to the power of negative 1 end exponent left parenthesis x right parenthesis
    Here, a is a constant and x is a variable.

    Now, we will differentiate the simplified function.
    fraction numerator d over denominator d x end fraction left square bracket t an to the power of negative 1 end exponent left parenthesis a right parenthesis space minus space tan to the power of negative 1 end exponent left parenthesis x right parenthesis right square bracket space equals space 0 space minus space fraction numerator 1 over denominator 1 space plus space x squared end fraction
left curly bracket space D e r i v a t i v e space o f space a space c o n s tan t space t e r m space i s space z e r o space
a n d space w e space u s e d space t h e space f o r m u l a space o f space d e r i v a t i v e space o f space tan to the power of negative 1 end exponent right curly bracket

fraction numerator d over denominator d x end fraction open square brackets tan to the power of negative 1 end exponent open parentheses fraction numerator a space minus space x over denominator 1 space plus space a x end fraction close parentheses close square brackets equals space minus fraction numerator 1 over denominator 1 space plus space x squared end fraction
    This is the final answer.

    For such questions, we should know different formulas.

    Related Questions to study

    General
    Maths-

    fraction numerator d over denominator d x end fraction open parentheses cosec to the power of negative 1 end exponent invisible function application open parentheses e to the power of 2 x plus 1 end exponent close parentheses close parentheses equals

    For such questions, we should know different formulas.

    fraction numerator d over denominator d x end fraction open parentheses cosec to the power of negative 1 end exponent invisible function application open parentheses e to the power of 2 x plus 1 end exponent close parentheses close parentheses equals

    Maths-General

    For such questions, we should know different formulas.

    General
    Maths-

    fraction numerator d over denominator d x end fraction open parentheses fraction numerator sin invisible function application x over denominator 1 plus c o s invisible function application x end fraction close parentheses equals

    The alternate method to solve this will be using u by method. It is method used in differentiation when we have a condition of numerator and denominator.

    fraction numerator d over denominator d x end fraction open parentheses fraction numerator sin invisible function application x over denominator 1 plus c o s invisible function application x end fraction close parentheses equals

    Maths-General

    The alternate method to solve this will be using u by method. It is method used in differentiation when we have a condition of numerator and denominator.

    General
    Maths-

    Locus of the foot of perpendicular fr om (-2,3) to a variable line with x intercept 2 is

    Locus of the foot of perpendicular fr om (-2,3) to a variable line with x intercept 2 is

    Maths-General
    parallel
    General
    Maths-

    Vertices of a triangle are (4, 3) , left parenthesis 5 blank s i n blank capital theta comma blank 5 blank c o s blank capital theta right parenthesis comma left parenthesis 5 blank c o s blank capital theta comma blank minus 5 blank s i n blank capital theta right parenthesis Then the locus of the orthocenter is

    Vertices of a triangle are (4, 3) , left parenthesis 5 blank s i n blank capital theta comma blank 5 blank c o s blank capital theta right parenthesis comma left parenthesis 5 blank c o s blank capital theta comma blank minus 5 blank s i n blank capital theta right parenthesis Then the locus of the orthocenter is

    Maths-General
    General
    Maths-

    A line through A(-5, -4) meets the line x+3y+2=0, 2x+y+4=0 and x-y-5=0 at B comma C and D respectively. If left parenthesis fraction numerator 15 over denominator A B end fraction right parenthesis to the power of 2 end exponent plus left parenthesis fraction numerator 10 over denominator A C end fraction right parenthesis to the power of 2 end exponent equals left parenthesis fraction numerator 6 over denominator A D end fraction right parenthesis to the power of 2 end exponent then the equation of the line is

    A line through A(-5, -4) meets the line x+3y+2=0, 2x+y+4=0 and x-y-5=0 at B comma C and D respectively. If left parenthesis fraction numerator 15 over denominator A B end fraction right parenthesis to the power of 2 end exponent plus left parenthesis fraction numerator 10 over denominator A C end fraction right parenthesis to the power of 2 end exponent equals left parenthesis fraction numerator 6 over denominator A D end fraction right parenthesis to the power of 2 end exponent then the equation of the line is

    Maths-General
    General
    Maths-

    If x subscript 1 end subscript comma x subscript 2 end subscript comma x subscript 3 end subscript as well as y subscript 1 end subscript comma y subscript 2 end subscript comma y subscript 3 end subscript are in G.P with the same common ratio, then the points left parenthesis x subscript 1 end subscript comma y subscript 1 end subscript right parenthesis comma left parenthesis x subscript 2 end subscript comma y subscript 2 end subscript right parenthesis comma left parenthesis x subscript 3 end subscript comma y subscript 3 end subscript right parenthesis .

    If x subscript 1 end subscript comma x subscript 2 end subscript comma x subscript 3 end subscript as well as y subscript 1 end subscript comma y subscript 2 end subscript comma y subscript 3 end subscript are in G.P with the same common ratio, then the points left parenthesis x subscript 1 end subscript comma y subscript 1 end subscript right parenthesis comma left parenthesis x subscript 2 end subscript comma y subscript 2 end subscript right parenthesis comma left parenthesis x subscript 3 end subscript comma y subscript 3 end subscript right parenthesis .

    Maths-General
    parallel
    General
    Maths-

    The range of alpha for which the points left parenthesis alpha comma 2 plus alpha right parenthesis and left parenthesis fraction numerator 3 alpha over denominator 2 end fraction comma alpha to the power of 2 end exponent right parenthesis lie on opposite side of the line 2x+3y=6 is

    The range of alpha for which the points left parenthesis alpha comma 2 plus alpha right parenthesis and left parenthesis fraction numerator 3 alpha over denominator 2 end fraction comma alpha to the power of 2 end exponent right parenthesis lie on opposite side of the line 2x+3y=6 is

    Maths-General
    General
    Maths-

    The internal bisectors of the a capital delta A B C, having the sides BC=3, CA=5 and AB =4 meet the sides BC, CA and AB in D, E and F respectively, the area of capital delta D E F is

    The internal bisectors of the a capital delta A B C, having the sides BC=3, CA=5 and AB =4 meet the sides BC, CA and AB in D, E and F respectively, the area of capital delta D E F is

    Maths-General
    General
    Maths-

    A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinate axes at points P and Q As L varies, the absolute minimum value of OP+OQ= where O is the origin

    A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinate axes at points P and Q As L varies, the absolute minimum value of OP+OQ= where O is the origin

    Maths-General
    parallel
    General
    Maths-

    Vertices of a variable triangle are (3, 4) left parenthesis 5 blank c o s blank theta comma blank 5 blank s i n blank theta right parenthesis and left parenthesis 5 blank s i n blank theta minus 5 blank c o s blank theta right parenthesis where theta element of R blankLocus of its orthocenter is

    Vertices of a variable triangle are (3, 4) left parenthesis 5 blank c o s blank theta comma blank 5 blank s i n blank theta right parenthesis and left parenthesis 5 blank s i n blank theta minus 5 blank c o s blank theta right parenthesis where theta element of R blankLocus of its orthocenter is

    Maths-General
    General
    Maths-

    If (0,0), (a, 2), (2, b) form the vertices of an equilateral triangle, where a and b not lie between 0 and 2, then the value of 4(aplusb)‐ab equals

    If (0,0), (a, 2), (2, b) form the vertices of an equilateral triangle, where a and b not lie between 0 and 2, then the value of 4(aplusb)‐ab equals

    Maths-General
    General
    Maths-

    The lines a x plus b y plus left parenthesis a alpha plus b right parenthesis equals 0 comma b x plus c y plus left parenthesis b alpha plus c right parenthesis equals 0 and left parenthesis a alpha plus b right parenthesis x plus left parenthesis b alpha plus c right parenthesis y equals 0 are concurrent if

    The lines a x plus b y plus left parenthesis a alpha plus b right parenthesis equals 0 comma b x plus c y plus left parenthesis b alpha plus c right parenthesis equals 0 and left parenthesis a alpha plus b right parenthesis x plus left parenthesis b alpha plus c right parenthesis y equals 0 are concurrent if

    Maths-General
    parallel
    General
    Maths-

    Equation of the line perpendicular to 4x + 7y + 9 = 0 and such that the triangle formed by it with the coordinates axes forms an area of 3.5 sq. units is

    Equation of the line perpendicular to 4x + 7y + 9 = 0 and such that the triangle formed by it with the coordinates axes forms an area of 3.5 sq. units is

    Maths-General
    General
    Maths-

    (0, 0) is the foot of the perpendicular from (4, 2) on a straight line. The equation of the line is

    (0, 0) is the foot of the perpendicular from (4, 2) on a straight line. The equation of the line is

    Maths-General
    General
    Maths-

    The orthocentre of the triangle having vertices at (2, 3) (2, 5) (4, 3) is

    The orthocentre of the triangle having vertices at (2, 3) (2, 5) (4, 3) is

    Maths-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.