Let f (x)= ex, g(x) - sin-1x andh (x) = f (g(x)), then h'(x)/h(x) = - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

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

Solution:

$\begin{array}{l} f (x) = e^{x} and g (x) = \sin^{- 1} x and h (x) = f (g (x)) \\ h (x) = f (\sin^{- 1} x) = e^{\sin^{- 1} x} \\ \Rightarrow h^{'} (x) = \frac{e^{\sin^{- 1} x}}{\sqrt{1 - x^{2}}} \Rightarrow \frac{h^{'} (x)}{h (x)} = \frac{1}{\sqrt{1 - x^{2}}} \end{array}$

Let f (x)= e^x, g(x) - sin^-1x andh (x) = f (g(x)), then h'(x)/h(x) =

Solution:

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