d dx e^ x x = - Vidyadip

MCQ

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

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

✓

Answer

Correct option: A.

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

a
(a) Let $y = {e^{x\sin x}}$==> $\log y = x\sin x$

$\therefore \frac{1}{y}\frac{{dy}}{{dx}} = \sin x + x\cos x$ or

$\frac{{dy}}{{dx}} = {e^{x\sin x}}(\sin x + x\cos x)$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $a, b, c$ are in harmonic progression, then straight line $\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0$ always passes through a fixed point, that point is

The derivative of $\tan ^{-1}\left(\frac{\sqrt{1+x^{2}}-1}{x}\right)$ with respect to $\tan ^{-1}\left(\frac{2 x \sqrt{1-x^{2}}}{1-2 x^{2}}\right)$ at $x=\frac{1}{2}$ is

Let $f: R \rightarrow R$ be a function defined $f ( x )=\frac{ x }{\left(1+ x ^4\right)^{1 / 4}}$ and $g ( x )= f ( f ( f ( f ( x ))))$ then $18 \int_0^{\sqrt{2 \sqrt{5}}} x^2 g(x) d x$

Let $\arg ( z )$ represent the principal argument of the complex number $z$. The, $| z |=3$ and $\arg ( z -1)-$ $\arg ( z +1)=\frac{\pi}{4}$ intersect

The cost function at American Gadget is $C(x) = x^3 - 6x^2 + 15x$ $(x$ in thousands of units and $x > 0)$ The production level at which average cost is minimum is

If area bounded by the curves ${y^2} = 4\,ax$ and $y = mx$ is ${a^2}/3,$, then the value of $m$ is

The solution of differential equation, $(x\,\cot \,y + \ln \,(\cos \,x))dy\, + \,(\ln \,(\sin \,y) - y\,\tan \,x)dx = 0$ is (where $C$ denotes constant of integration)

If $A_1, A_3, ..... A_{2n - 1}$ are $n$ skew symmetric matrices of same order then $B =$$\sum\limits_{r = 1}^n {(2r - 1){{({A_{2r - 1}})}^{2r - 1}}} $ will be

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls, one in each box, could be placed such that a ball does not go to box of its own colour is

If $A$ and $B$ are sets, then $A \cap (B -A)$ is