Search any question & find its solution
Question:
Answered & Verified by Expert
If $f(x)=\int_{x^2}^{x^4} \sin \sqrt{t} d t$, then $f^{\prime}(x)$ equals
Options:
Solution:
1577 Upvotes
Verified Answer
The correct answer is:
$4 x^3 \sin x^2-2 x \sin x$
We have $f(x)=\int_{x^2}^{x^4} \sin \sqrt{t} d t$
$\begin{aligned} \therefore \quad f^{\prime}(x) & =\frac{d}{d x}\left(x^4\right)\left(\sin \sqrt{x^4}\right)-\frac{d}{d x}\left(x^2\right)\left(\sin \sqrt{x^2}\right) \\ & =4 x^3 \sin x^2-2 x \sin x\end{aligned}$
$\begin{aligned} \therefore \quad f^{\prime}(x) & =\frac{d}{d x}\left(x^4\right)\left(\sin \sqrt{x^4}\right)-\frac{d}{d x}\left(x^2\right)\left(\sin \sqrt{x^2}\right) \\ & =4 x^3 \sin x^2-2 x \sin x\end{aligned}$
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.