Differentiation Question 290
Question: Let $ f(x)=e^{x} $ , $ g(x)={{\sin }^{-1}}x $ and $ h(x)=f(g(x)), $ then $ h’(x)/h(x)= $
[EAMCET 2002]
Options:
A) $ {e^{{{\sin }^{-1}}x}} $
B) $ 1/\sqrt{1-x^{2}} $
C) $ {{\sin }^{-1}}x $
D) $ 1/(1-x^{2}) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x)=e^{x} $ and $ g(x)={{\sin }^{-1}}x $ and $ h(x)=f(g(x)) $
Therefore $ h(x) $ = $ f({{\sin }^{-1}}x)={e^{{{\sin }^{-1}}x}} $
\ $ h(x)={e^{{{\sin }^{-1}}}}x $
Therefore $ {h}’(x)={e^{{{\sin }^{-1}}x}}.\frac{1}{\sqrt{1-x^{2}}} $
Therefore $ \frac{{h}’(x)}{h(x)}=\frac{1}{\sqrt{1-x^{2}}} $ .
BETA
