differentiate the following function with respect to x

(1) sin^-1(x/sqrt(x^2+a^2)

(2)sin^-1(2x^2 – 1),0

(3) sin^-1(1-2x^2)0

Y=sin^-1v(1-x²)

Dy/dx=1/v1-(1-x²) .{-2x/v(1-x²)}

=-1/v(1-x²)

Y=sin^-1x/v(x²+a²)

Dy/dx=[1/v1-{x/v(x²+a²)}²].[{v(x²+a²).1-x.2x/v(x²+a²)}/(x²+a²)]

=a/(x²+a²)

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty

Hi