Question

Find `dy/dx if y=cos^-1(sqrt(x))`

Answer 1

`"Let" y=cos^(-1)sqrtx`

Differentiating w.r.t x

`dy/dx=d/dx(cos^(-1)sqrtx)`

`=-1/(sqrt(1-(sqrtx)^2))d/dx(sqrtx)`

`=-1/sqrt(1-x)xx1/(2sqrtx)`

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