The differential of e^ x^3 with respect to x is - Vidyadip

MCQ

The differential of ${e^{{x^3}}}$ with respect to $\log x$ is

A
${e^{{x^3}}}$
B
$3{x^2}{e^{{x^3}}}$
✓
$3{x^3}{e^{{x^3}}}$
D
$3{x^2}{e^{{x^3}}} + 3{x^2}$

✓

Answer

Correct option: C.

$3{x^3}{e^{{x^3}}}$

c
(c) $y = {e^{{x^3}}}$, $z = \log x$

==> $\frac{{dy}}{{dx}} = {e^{{x^3}}}\,.\,(3{x^2}) = 3{x^2}{e^{{x^3}}}$ .....$(i)$

and $\frac{{dz}}{{dx}} = \frac{1}{x}$ ....$(ii)$

==> $\frac{{dy}}{{dz}} = \frac{{3{x^2}{e^{{x^3}}}}}{{\left( {1/x} \right)}} = 3{x^3}{e^{{x^3}}}$.

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

If $\int\frac{1}{(\text{x}+2)(\text{x}^2+1)}\text{ dx}=\text{a}\log|1+\text{x}^2|+\text{b}\tan^{-1}\text{x}+\frac{1}{5}\log|\text{x}+2|+\text{C},$ then

$\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
$\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$
$\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
$\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$

The lines $\frac{x-2}{2}=\frac{y}{-2}=\frac{z-7}{16}$ and $\frac{x+3}{4}=\frac{y+2}{3}=\frac{z+2}{1}$ intersect at the point $P$. If the distance of $P$ from the line $\frac{x+1}{2}=\frac{y-1}{3}=\frac{z-1}{1}$ is $l$, then $14 l^2$ is equal to.................

$\int_{}^{} {\sqrt {1 + \cos x} \;dx} $ equals

The shortest distance between the line $y = x$ and the curve $y^2 = x - 2$ is

Which of the following functions form Z to itself are bijections?

f(x) = x³
f(x) = x + 2
f(x) = 2x + 1
f(x) = x² + x

Choose the correct answer from the given four options.
Let A and B be two events such that $\text{P}(\text{A})=\frac{3}{8},\text{P}({\text{B}})=\frac{5}{8}$ and $\text{P}(\text{A}\cup\text{B})=\frac{3}{4}.$Then $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)\cdot\text{P}\Big(\frac{\text{A'}}{\text{B}}\Big)$ is equal to:

$\frac{2}{5}$
$\frac{3}{8}$
$\frac{3}{20}$
$\frac{6}{25}$

Let $\vec p\, = \,2\hat i\, + \,3\hat j\, + \,a\hat k$, $\vec q\, = \,b\hat i\, + \,5\hat j\, - \hat k$, $\vec r\, = \,\hat i\, + \,\hat j\, + 3\hat k$ . If $\vec p,\vec q,\vec r$ are coplanar and $\vec p,\vec q$= $20$ , then the ordered pair $(a, b)$ is

The solution of the differential equation $\frac{{dy}}{{dx}} + y\cot x = 2\cos x$ is

The minimum distance of a point on the curve $y = x^2 - 4$ from the origin is

Let $a, b$ and $c$ be positive constants. The value of $‘a’$ in terms of $‘c’$ if the value of integral $\int\limits_0^1 {(ac{x^{b + 1}} + {a^3}b{x^{3b + 5}})\,dx} $ is independent of $b$ equals