Home
Class 12
MATHS
Find (dy)/(dx) in the following:sin^2x+...

Find `(dy)/(dx)` in the following:`sin^2x+cos^2y=1`

Text Solution

Verified by Experts

`sin^2x+cos^2y=1`

Differentiating both sides w.r.t. x

`(d(sin^2x+cos^2y))/dx=(d(1))/dx`

`(d(sin^2x))/dx+(d(cos^2y))/dx=0`

Calculating derivative of `sin^2x` and `cos^2y` separately.

Finding Derivative of `sin^2x`

`(d(sin^2x))/dx=2sin^(2-1)x.(d(sinx))/dx`

`(d(sin^2x))/dx=2sinx.(d(sinx))/dx`

`(d(sin^2x))/dx=2sinxcosx`

Finding Derivative of `cos^2y`

`(d(cos^2y))/dx=2cos^(2-1)y.d/dx(cosy)`

`(d(cos^2y))/dx=2cosy.(-siny)dy/dx`

`(d(cos^2y))/dx=-2cosysiny.dy/dx`

Now,

`(d(sin^2x))/dx+(d(cos^2y))/dx=0`

`2sinxcosx+(-2cosysiny.dy/dx)=0`

`2sinxcosx-2siny.cosy.dy/dx=0`

`-2siny.cosy.dy/dx=-2sinxcosx`

`-sin2y.dy/dx=-sin2x`

`dy/dx=(-sin2x)/(-sin2y)`

`dy/dx=(sin2x)/(sin2y)`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise EXERCISE 5.8|6 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise EXERCISE 5.5|18 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise EXERCISE 5.4|10 Videos

  • APPLICATION OF INTEGRALS

    NCERT|Exercise EXERCISE 8.2|7 Videos

  • DETERMINANTS

    NCERT|Exercise EXERCISE 4.4|5 Videos

Similar Questions

Explore conceptually related problems

Find (dy)/(dx) in the following: 2x+3y=sin y

Find (dy)/(dx) in the following: y=sin^(-1)(2x sqrt(1-x^(2))),-(1)/(sqrt(2))

Find (dy)/(dx) in the following: y=sin^(-1)((1-x^(2))/(1+x^(2))),0

Find (dy)/(dx) in the following: y=sin^(-1)((2x)/(1+x^(2)))

Find (dy)/(dx) in the following 2x + 3y = sin x

Find (dy)/(dx) in the following: 1.2x+3y=sin x2.2x+3y=sin y3.ax+by^(2)=cos y

Find (dy)/(dx) in the following: 1.2x+3y=sin x2.2x+3y=sin y3.ax+by^(2)=cos y

Find (dy)/(dx) for the function: y=a^((sin^(-1)x)^(2))

Find (dy)/(dx) for y=sin(x^(2)+1)

Find (dy)/(dx) if y=sin(x^(2))