HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

If y=cos^-1(2xsqrt(1-x^2)), find dy/dx - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

Login
Create free account


      Forgot password?

Question

If `y=cos^-1(2xsqrt(1-x^2))`, find dy/dx

Solution

`y=cos^-1(2xsqrt(1-x^2))`

put `x=sintheta`

`theta =sin^-1x`

`y=cos^-1(2xsqrt(1-x^2))`

`=cos^-1(2sinthetasqrt(1-sin^2theta))`

`=cos^-1(2sintheta costheta)`

`=cos^-1(sin2theta)`

`=cos^-1(cos(pi/2-2theta))`

`y=pi/2-2theta=pi/2-2sin^-1x`

Differentiating with respect to 'x', we get

`dy/dx=-2/sqrt(1-x^2)`

 

  Is there an error in this question or solution?

APPEARS IN

 2015-2016 (March) (with solutions)
Question 6.1.3 | 3.00 marks
Solution If y=cos^-1(2xsqrt(1-x^2)), find dy/dx Concept: Derivative - Derivative of Inverse Function.
S
View in app×