Question

If f (x) = sin−1x, then f′(√3/2)= ?

Answer 1

`f'((\sqrt3)/(2))` = 2

Step-by-step explanation:

Given that,

`f(x)=\sin^(-1) x`

We need to find the value of
`f'((\sqrt3)/(2))`

First, we take f'(x). We know that,

`(d)/(dx)(\sin^(-1) x)=(1)/(√(1-x^2) )\\\\f'(x)=(1)/(√(1-x^2) )\\\\f'((\sqrt3)/(2))=\frac{1}{\sqrt{1-((\sqrt3)/(2))^2} }\\\\=\frac{1}{\sqrt{1-((3)/(4))} }\\\\=\frac{1}{\sqrt{(1)/(4)}}\\\\=(1)/((1)/(2))\\\\=2`

So, the value of
`f'((\sqrt3)/(2))` is 2.