If A = 2^x x x , then dA dx = - Vidyadip

MCQ

If $A = {{{2^x}\cot x} \over {\sqrt x }},$ then ${{dA} \over {dx}} = $

✓
${{{2^{x - 1}}\left\{ { - 2x\,{\rm{cos}}{\rm{e}}{{\rm{c}}^2}x + \cot x.\log \left( {{{{4^x}} \over e}} \right)} \right\}} \over {{x^{3/2}}}}$
B
${{{2^{x - 1}}\left\{ { - 2x\cos {\rm{e}}{{\rm{c}}^2}x + \cot x.\log \left( {{{{4^x}} \over e}} \right)} \right\}} \over x}$
C
${{2x\left\{ { - 2x{\rm{cose}}{{\rm{c}}^2}x + \cot x.\log \left( {{{{4^x}} \over e}} \right)} \right\}} \over {{x^{{\rm{3/2}}}}}}$
D
None of these

✓

Answer

Correct option: A.

${{{2^{x - 1}}\left\{ { - 2x\,{\rm{cos}}{\rm{e}}{{\rm{c}}^2}x + \cot x.\log \left( {{{{4^x}} \over e}} \right)} \right\}} \over {{x^{3/2}}}}$

a
(a) $\frac{{dA}}{{dx}} = \frac{{\sqrt x \{ {2^x}{{\log }_e}2\cot x - {2^x}{\rm{cose}}{{\rm{c}}^2}x\} - {2^x}\cot x\frac{1}{{2\sqrt x }}}}{x}$

$ = \frac{{{2^{x - 1}}\left\{ { - 2x\,{\rm{cose}}{{\rm{c}}^2}x + \cot x.\log \left( {\frac{{{4^x}}}{e}} \right)} \right\}}}{{{x^{3/2}}}}$.

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

A bag contain 4 white and 2 black balls. Two balls are drawn at random. The probability that they are of the same colour is ________.

If a matrix $A$ is both symmetric and skewsymmetric, then

If f(x) = (ax² – b)³, then the function g such that f{g(x)} = g{f(x)} is given by:

$\text{g(x)}=\Big(\frac{\text{b}-\text{x}^\frac{1}{3}}{\text{a}}\Big)^\frac{1}{2}$
$\text{g(x)}=\frac{1}{(\text{ax}^2+\text{b})^3}$
$\text{g(x)}=(\text{ax}^2+\text{b})^\frac{1}{3}$
$\text{g(x)}=\Big(\frac{\text{x}^\frac{1}{3}+\text{b}}{\text{a}}\Big)^\frac{1}{2}$

If ${A_\lambda } = \left( {\begin{array}{*{20}{c}}
\lambda &{\lambda - 1}\\
{\lambda - 1}&\lambda
\end{array}} \right);\,\lambda \in N$ then $|A_1| + |A_2| + ..... + |A_{300}|$ is equal to

A and B are two events. $P ( A )=\frac{1}{2}, P ( B )=\frac{1}{3}$ and $P ( A \cap B )=\frac{1}{4}$ then $P \left( A ^{\prime} / B \right)=$ _________.

Which of the following equation is linear

Choose the correct answer from the given four options.
If A and B are two independent events with $\text{P}(\text{A})=\frac{3}{5}$ and $\text{P}(\text{A})=\frac{4}{9},$ then $\text{P}(\text{A'}\cap\text{B'})$ equals:

$\frac{4}{15}$
$\frac{8}{45}$
$\frac{1}{3}$
$\frac{2}{9}$

If $P\,(A) = \frac{1}{2},\,\,P\,(B) = \frac{1}{3}$ and $P\,(A \cap B) = \frac{1}{4},$ then $P\,\left( {\frac{B}{A}} \right) = $

If $\text{A} = \begin{bmatrix}\cos\alpha&-\sin\alpha\\ \sin\alpha&\cos\alpha\end{bmatrix},\text{then}\ \text{A + A}'=\text{I}$, if the value of a is:

$\frac{\pi}{6}$
$\frac{\pi}{3}$
$\text{n}$
$\frac{3\pi}{2}$

The value of $\int_0^2 {\frac{{{3^{\sqrt x }}}}{{\sqrt x }}} \,dx$ is