Search any question & find its solution
Question:
Answered & Verified by Expert
If $f(\mathrm{x})=\tan \mathrm{x}+\mathrm{e}^{-2 \mathrm{x}}-7 \mathrm{x}^{3}$, then what is the value of $f^{\prime}(0)$?
Options:
Solution:
1859 Upvotes
Verified Answer
The correct answer is:
$-1$
Given $f(x)=\tan x+e^{-2 x}-7 x^{3}$
On differentiating w.r.t. $\mathrm{x}$, we get
$f^{\prime}(x)=\sec ^{2} x-2 e^{-2 x}-21 x^{2}$
Put $x=0$
$\Rightarrow f^{\prime}(0)=\sec ^{2} 0-2 e^{0}-21 \times 0=1-2=-1$
On differentiating w.r.t. $\mathrm{x}$, we get
$f^{\prime}(x)=\sec ^{2} x-2 e^{-2 x}-21 x^{2}$
Put $x=0$
$\Rightarrow f^{\prime}(0)=\sec ^{2} 0-2 e^{0}-21 \times 0=1-2=-1$
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.