Question

Let $f\left(\right.x\left.\right)=e^{x},g\left(\right.x\left.\right)=\left(sin\right)^{- 1}x$ and $h\left(\right.x\left.\right)=f\left(\right.g\left(\right.x\left.\right)\left.\right)$ then $h^{'}\left(\right.x\left.\right)/h\left(\right.x\left.\right)=$

• A. $e^{sin^{- 1} x}$
• B. $1/\sqrt{1 - x^{2}}$
• C. $sin^{- 1}x$
• D. $1/\left(1 - x^{2}\right)$

Answer 1

Answer: (B)

$f ( x )= e ^{ x }$ and $g ( x )=\sin ^{-1} x$ and $h ( x )= f ( g ( x ))$
$\Rightarrow h ( x )= f \left(\sin ^{-1} x \right)= c ^{\sin ^{-1} x }$
$\Rightarrow h ( x )=\frac{ e ^{\sin ^{-1} x }}{\sqrt{1- x ^2}}$
$\Rightarrow \frac{ h ( x )}{ h ( x )}=\frac{1}{\sqrt{1- x ^2}}$