Differentiation Question 283
Question: If $ f(1)=3,{f}’(1)=2, $ then $ \frac{d}{dx}{\log f(e^{x}+2x)} $ at $ x=0 $ is
[AMU 1999]
Options:
A) 2 / 3
B) 3 / 2
C) 2
D) 0
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ y=\frac{d}{dx}{\log f(e^{x}+2x)}=\frac{{f}’(e^{x}+2x)(e^{x}+2)}{f(e^{x}+2x)} $
$ \therefore {{(y)} _{x=0}} $ = $ \frac{1}{f(1)}.{f}’(1).3 $ = $ \frac{2}{3}.3=2 $ .
BETA
