Applications Of Derivatives Question 162
Question: The rate of change of $ \sqrt{(x^{2}+16)} $ with respect to $ \frac{x}{x-1} $ at $ x=3 $ is
[AMU 2001; MP PET 1987]
Options:
A) 2
B) $ \frac{11}{5} $
C) $ -\frac{12}{5} $
D) $ -3 $
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ y=\sqrt{x^{2}+16} $ and $ z=\frac{x}{x-1} $
therefore $ \frac{dy}{dx}=\frac{1}{2}{{(x^{2}+16)}^{-1/2}}(2x) $ & $ \frac{dz}{dx}=\frac{x-1-x}{{{(x-1)}^{2}}}=\frac{-1}{{{(x-1)}^{2}}} $ \ $ \frac{dy}{dz}=\frac{-x}{\sqrt{x^{2}+16}},\frac{1}{1/{{(x-1)}^{2}}} $
$ {{( \frac{dy}{dz} )}_{x=3}}=\frac{-3{{(2)}^{2}}}{5}=\frac{-12}{5} $ .
BETA
