Question

Diffrentiate with respect to x​

Answer 1

Question:-To differenitaiate y=Sin^2x/(1+cos^2x)<with respect to x

Solution:-To solve this question,we have to use quotient rule of differenitaiation....

=>dy/dx={sin^2x}'(1+cos^2x)-(1+cos^2x)'(sin^2x)}/(1+cos^2x)^2

=>dy/dx=2sinxcosx{1+cos^2x}-(-2cosxsinx)(sin^2x)/{1+cos^2x)^2

=>dy/dx=2sinxcosx+2sinxcos^3x+2cosxsin^3x/(1+cos^2x)^2

Taking 2sinxcosx common from numerator

=>dy/dx=2sinxcosx{cos^2x+sin^2x)/(1+cos^2x)^2

=>dy/dx=2sinxcosx/(1+cos^2x)^2

=>dy/dx=Sin2x/(1+cos^2x)^2

Hence this will be the required answer

{hope it helps you}