d dx ( x^2 e^x x) = - Vidyadip

MCQ

${d \over {dx}}({x^2}{e^x}\sin x) = $

✓
$x\,{e^x}(2\sin x + x\sin x + x\cos x)$
B
$x\,{e^x}(2\sin x + x\sin x - \cos x)$
C
$x\,{e^x}(2\sin x + x\sin x + \cos x)$
D
None of these

✓

Answer

Correct option: A.

$x\,{e^x}(2\sin x + x\sin x + x\cos x)$

a
(a) $\frac{d}{{dx}}\left( {{x^2}{e^x}\sin x} \right) = {x^2}\frac{d}{{dx}}\left( {{e^x}\sin x} \right)$$ + {e^x}\sin x\frac{d}{{dx}}({x^2})$

$= x{e^x}(2\sin x + x\sin x + x\cos x)$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int\limits_{ - \,1}^1 {\,\,\frac{{{x^3}\, + \,\,|x|\,\, + \,\,1}}{{{x^2}\, + \,\,2\,|x|\,\, + \,\,1}}}\,dx$ $= a\, ln\, 2 + b$ then :

The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2 \hat{i}+\hat{j}+\hat{k}, \hat{i}-\lambda^2 \hat{j}+\hat{k}$ and $\hat{i}+\hat{j}-\lambda^2 \hat{k}$ are coplanar, is

If $|a \times b|\, = 4$ and $|a\,.\,b|\, = 2$, then $|a{|^2}\,\,|b{|^2} = $

If $A = \left( {\begin{array}{*{20}{c}}i&1\\0&i\end{array}} \right)$, then ${A^4}$ equals

The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius $ = \sqrt 3 $ is

The area bounded by the curve $y = x^2 - 1$ $\&$ the straight line $x + y = 3$ is :

The domain of $f(x) = [\sin x] \cos \left( {\frac{\pi }{{[x - 1]}}} \right)$ is (where $[.]$ denotes $G.I.F.$)

If $\text{y}=\Big(1+\frac{1}{\text{x}}\Big)^\text{x},$ then $\frac{\text{dy}}{\text{dx}}=$

$\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\Big(\text{x}+\frac{1}{\text{x}}\Big)-\frac{1}{\text{x}+1}$
$\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\log\Big(1+\frac{1}{\text{x}}\Big)$
$\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\Big\{\log(\text{x}+1)-\frac{\text{x}}{\text{x}+1}\Big\}$
$\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\Big\{\log\Big(\text{x}+\frac{1}{\text{x}}\Big)-\frac{1}{\text{x}+1}\Big\}$

The principal solution of $\tan ^{-1}\left(\tan \left(\frac{7 \pi}{6}\right)\right)$ is

If $A=\left[\begin{array}{cc}2 & 3 \\ 0 & -1\end{array}\right],$ then the value of $\operatorname{det}\left( A ^{4}\right)+\operatorname{det}\left( A ^{10}-(\operatorname{Adj}(2 A ))^{10}\right)$ is equal to ........