If y = (x ^3 x)^ 3/2 , then dy dx = - Vidyadip

MCQ

If $y = {(x{\cot ^3}x)^{3/2}},$ then ${{dy} \over {dx}} = $

✓
${3 \over 2}{(x{\cot ^3}x)^{1/2}}[{\cot ^3}x - 3x{\cot ^2}x\cos {\rm{e}}{{\rm{c}}^2}x]$
B
${3 \over 2}{(x{\cot ^3}x)^{1/2}}[{\cot ^2}x - 3x{\cot ^2}x\,{\rm{cose}}{{\rm{c}}^2}x]$
C
${3 \over 2}{(x{\cot ^3}x)^{1/3}}[{\cot ^3}x - 3x\,{\rm{cos}}{\rm{e}}{{\rm{c}}^2}x]$
D
${3 \over 2}{(x{\cot ^3}x)^{3/2}}[{\cot ^3}x - 3x\,{\rm{cos}}{\rm{e}}{{\rm{c}}^2}x]$

✓

Answer

Correct option: A.

${3 \over 2}{(x{\cot ^3}x)^{1/2}}[{\cot ^3}x - 3x{\cot ^2}x\cos {\rm{e}}{{\rm{c}}^2}x]$

a
(a) $y = {(x{\cot ^3}x)^{3/2}}$

$\therefore \frac{{dy}}{{dx}} = \frac{3}{2}{(x{\cot ^3}x)^{1/2}}[{\cot ^3}x + 3x{\cot ^2}x( - {\rm{cose}}{{\rm{c}}^2}x)]$

$ = \frac{3}{2}{(x{\cot ^3}x)^{1/2}}[{\cot ^3}x - 3x{\cot ^2}x\,{\rm{cose}}{{\rm{c}}^2}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 STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $f(x)=1-\frac{1}{\text{x}},$ then $\text{f}(\text{f}(\frac{1}{\text{x}}))$

If the length of the perpendicular drawn from the point $P ( a , 4,2), a >0$ on the line $\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}$ is $2 \sqrt{6}$ units and $Q \left(\alpha_{1}, \alpha_{2}, \alpha_{3}\right)$ is the image of the point $P$ in this line, then $a+\sum_{i=1}^{3} \alpha_{i}$ is equal to.

Choose the correct answer from the given four option.
The solution of the differential equation $\frac{\text{d}\text{y}}{\text{d}\text{x}}=\frac{1+\text{y}^2}{1+\text{x}^2}$ is:

If $\times $ is a binary operation on set of integers $I$ defined by $a \times b = 3a + 4b - 2,$ then find the value of $4 \times 5.$

The differential coefficient of ${\tan ^{ - 1}}\left( {{{\sqrt {1 + {x^2}} - 1} \over x}} \right)$ with respect to ${\tan ^{ - 1}} x$ is

If ${x^2} + {y^2} + {z^2} = {r^2}$, then ${\tan ^{ - 1}}\left( {\frac{{xy}}{{zr}}} \right) + $ ${\tan ^{ - 1}}\left( {\frac{{yz}}{{xr}}} \right) + {\tan ^{ - 1}} \left( {\frac{{zx}}{{yr}}} \right) = $

Find the cofactor of element -3 in the determinant $\triangle=\begin{bmatrix}1&4&4\\-3&5&9\\2&1&2\end{bmatrix}$ is:

The system of equations $x + y + z = 6$, $x + 2y + 3z = 10,x + 2y + \lambda z = \mu $, has no solution for

The value of $\int\limits_0^{\frac{\pi }{2}} {\sin \,8x\,\cot\, xdx\, + \int\limits_{ - \frac{\pi }{4}}^{\frac{\pi }{4}} {\ln \left( {\frac{{1 - \sin \,x}}{{1 + \sin \,x}}} \right)dx} } $ is equal to

The constraints $-x+y \leq 1,-x+3 y \leq 9, x \geq 0, y \geq 0$ defines on $.....$