# If y=cos^-1(2xsqrt(1-x^2)), find dy/dx - Mathematics and Statistics

Sum

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

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

=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=0 -2/sqrt(1-x^2) = (-2)/sqrt(1-x^2)

Concept: The Concept of Derivative - Derivative of Inverse Function
Is there an error in this question or solution?