Question #1cabe

1 Answer
Apr 21, 2017

f'(x)=4arcsin(x)1/(sqrt(1-x^2))

Explanation:

By chain rule

f'(x)=4arcsin(x) (arcsin(x))'

To calculate (arcsin(x))' use the inverse rule:

y=f^{-1}(x)\Rightarrow y'=1/(f'(y))

Hence if y=arcsin(x), we have x=sin(y), x'=cos(y), hence y'=1/cos(y)=1/cos(arcsin(x)).

In order to compute cos(arcsin(x)), consider

cos^2(arcsin(x))+sin^2(arcsin(x))=1, but sin^2(arcsin(x))=x^2, hence

cos(arcsin(x))=sqrt(1-x^2). Hence we get the answer