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Maths-

General

Easy

Question

If x^y y^x = 1, then $fraction numerator d y over denominator d x end fraction$ is :

$\frac{y (y + x \log y)}{x (y \log x + x)}$
$\frac{y (x + y \log x)}{x (y + x \log y)}$
$- \frac{y (y + x \log y)}{x (y \log x + x)}$
none of these

The correct answer is: $negative fraction numerator y left parenthesis y plus x log invisible function application y right parenthesis over denominator x left parenthesis y log invisible function application x plus x right parenthesis end fraction$

x^y y^x = 1Þy log x + x log y = 0
Þ $fraction numerator y over denominator x end fraction plus log invisible function application x fraction numerator d y over denominator d x end fraction plus x. fraction numerator 1 over denominator y end fraction fraction numerator d y over denominator d x end fraction plus log invisible function application y.1 equals 0$ Þ $open parentheses log invisible function application x plus fraction numerator x over denominator y end fraction close parentheses fraction numerator d y over denominator d x end fraction equals negative open square brackets log invisible function application y plus fraction numerator y over denominator x end fraction close square brackets$
Þ $fraction numerator y log invisible function application x plus x over denominator y end fraction fraction numerator d y over denominator d x end fraction equals negative fraction numerator x log invisible function application y plus y over denominator x end fraction$ Þ $fraction numerator d y over denominator d x end fraction equals negative fraction numerator y over denominator x end fraction open parentheses fraction numerator y plus x log invisible function application y over denominator y log invisible function application x plus x end fraction close parentheses$

Related Questions to study

If g(x) is a polynomial such that g(x) g(y) = g(x) + g(y) + g(xy) − 2 for all real x and y and g(2) = 5, then $stack l i m with x rightwards arrow 2 below g ´ left parenthesis x right parenthesis$ is :

If g(x) is a polynomial such that g(x) g(y) = g(x) + g(y) + g(xy) − 2 for all real x and y and g(2) = 5, then $stack l i m with x rightwards arrow 2 below g ´ left parenthesis x right parenthesis$ is :

$CH subscript 3 CH equals CHCH subscript 3 plus KCl plus straight H subscript 2 straight O$ Dehydrohalogenation reaction of 2-chlorobutane gives 2-butene.
(R) Elimination reaction takes' place according to Saytzeff's rule.

$CH subscript 3 CH equals CHCH subscript 3 plus KCl plus straight H subscript 2 straight O$ Dehydrohalogenation reaction of 2-chlorobutane gives 2-butene.
(R) Elimination reaction takes' place according to Saytzeff's rule.

Chemistry-General

(R) -CN is an ambident nucleophile, therefore, reaction gives both cyanide and isocyanide.

(R) -CN is an ambident nucleophile, therefore, reaction gives both cyanide and isocyanide.

Chemistry-General

parallel

If 1,3-dibromopropane reacts with zinc and NaI, the product. obtained is : .

If 1,3-dibromopropane reacts with zinc and NaI, the product. obtained is : .

Chemistry-General

In the following reaction, .

The major product obtained is :

In the following reaction, .

The major product obtained is :

Chemistry-General

For the following reaction,

product [A] is:

For the following reaction,

product [A] is:

Chemistry-General

parallel

When 2-chloro-2-methylbutane is heated with alcoholic KOH, the possible product/s is/are:
i) $open parentheses C H subscript 3 end subscript close parentheses subscript 2 end subscript C equals C H C H subscript 3 end subscript$
ii) $H subscript 2 end subscript C equals stack C with bar on top open parentheses C H subscript 3 end subscript close parentheses stack C with bar on top H subscript 2 end subscript C H subscript 3 end subscript$
iii) $open parentheses C H subscript 3 end subscript close parentheses subscript 2 end subscript C H C H equals C H subscript 2 end subscript$

When 2-chloro-2-methylbutane is heated with alcoholic KOH, the possible product/s is/are:
i) $open parentheses C H subscript 3 end subscript close parentheses subscript 2 end subscript C equals C H C H subscript 3 end subscript$
ii) $H subscript 2 end subscript C equals stack C with bar on top open parentheses C H subscript 3 end subscript close parentheses stack C with bar on top H subscript 2 end subscript C H subscript 3 end subscript$
iii) $open parentheses C H subscript 3 end subscript close parentheses subscript 2 end subscript C H C H equals C H subscript 2 end subscript$

Chemistry-General

(A) predominantly is:

(A) predominantly is:

Chemistry-General

Ethyl chloride on reduction with $L i A l H subscript 4 end subscript$ gives compound , X' as an important product. 'X' on chlorination with one mole of Cl₂ in the presence of light at ordinary temperature gives' Y'. What is 'Y' ?

Ethyl chloride on reduction with $L i A l H subscript 4 end subscript$ gives compound , X' as an important product. 'X' on chlorination with one mole of Cl₂ in the presence of light at ordinary temperature gives' Y'. What is 'Y' ?

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parallel

(X) is:

(X) is:

Chemistry-General

Which can undergo haloform reaction?

Which can undergo haloform reaction?

Chemistry-General

when treated with two equivalents of sodium in dry ether gives:

when treated with two equivalents of sodium in dry ether gives:

Chemistry-General

parallel

the major product formed in the following reaction,
is:

the major product formed in the following reaction,
is:

Chemistry-General

Which of the following is liquid at room .temperature?

Which of the following is liquid at room .temperature?

Chemistry-General

$stack L t with x rightwards arrow 1 below open square brackets fraction numerator x to the power of 3 end exponent plus 2 x to the power of 2 end exponent plus x plus 1 over denominator x to the power of 2 end exponent plus 2 x plus 3 end fraction close square brackets to the power of fraction numerator 1 minus cos invisible function application left parenthesis x minus 1 right parenthesis over denominator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end fraction end exponent$ is

$stack L t with x rightwards arrow 1 below open square brackets fraction numerator x to the power of 3 end exponent plus 2 x to the power of 2 end exponent plus x plus 1 over denominator x to the power of 2 end exponent plus 2 x plus 3 end fraction close square brackets to the power of fraction numerator 1 minus cos invisible function application left parenthesis x minus 1 right parenthesis over denominator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end fraction end exponent$ is

parallel

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