Search any question & find its solution
Question:
Answered & Verified by Expert
If $f(x)=\cos x, g(x)=\log x$ and $y=($ gof $)(x)$, then what is the value of $\frac{d y}{d x}$ at $x=0 ?$
Options:
Solution:
1808 Upvotes
Verified Answer
The correct answer is:
0
Given $f(x)=\cos x$ and $g(x)=\log x$
Consider $\mathrm{y}=\operatorname{gof}(x)$
$\quad=g(f(x)\}$
$\quad=\log (f(x))$
$\quad=\log (\cos x)$
$\therefore \frac{d y}{d x}=\frac{1}{\cos x}(-\sin x)=-\tan x$
$\Rightarrow\left(\frac{d y}{d x}\right)_{x=0}=-\tan 0=0$
Consider $\mathrm{y}=\operatorname{gof}(x)$
$\quad=g(f(x)\}$
$\quad=\log (f(x))$
$\quad=\log (\cos x)$
$\therefore \frac{d y}{d x}=\frac{1}{\cos x}(-\sin x)=-\tan x$
$\Rightarrow\left(\frac{d y}{d x}\right)_{x=0}=-\tan 0=0$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.