Let f(x)=ex, g(x)=sin−1x and h(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
$\frac{1}{\sqrt{1 - x^{2}}}$
C
$\sin^{- 1} x$
D
$\frac{1}{(1 - x^{2})}$

Solution:

$f (x) = e^{x} and g (x) = \sin^{- 1} x and h (x) = f (g (x))$

$\Rightarrow h (x) = f (\sin^{- 1} x) = e^{\sin^{- 1} x}$

$∴ h (x) = e^{\sin^{- 1}} x \Rightarrow h^{'} (x) = e^{\sin^{- 1} x} \cdot \frac{1}{\sqrt{1 - x^{2}}} \Rightarrow \frac{h^{'} (x)}{h (x)} = \frac{1}{\sqrt{1 - x^{2}}} .$

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

Solution:

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