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

MCQ

If $y = \cos (\sin {x^2}),$ then at $x = \sqrt {{\pi \over 2}} ,{{dy} \over {dx}}=$

A
$-2$
B
$2$
C
$ - 2\sqrt {{\pi \over 2}} $
✓
$0$

✓

Answer

Correct option: D.

$0$

d
(d) Since $\frac{{dy}}{{dx}} = - \sin (\sin {x^2}).\cos {x^2}.2x$

Therefore, at $x = \sqrt {\frac{\pi }{2}} ,$ $\cos {x^2} = \cos \frac{\pi }{2} = 0$

$\Rightarrow $ $\frac{{dy}}{{dx}} = 0$.

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

Function $f(x) = \left\{ {\begin{array}{*{20}{c}} {sgn \left( {\left[ x \right]} \right)\,\,\,\,;\,\,\,x \ne I} \\ {\left[ {sgn \left( x \right)} \right]\,\,\,;\,\,\,x = I} \end{array}} \right.$ is '( where $sgn ()$ denotes signum function $and$ $[.]$ denotes greatest integer function )

If $\int \limits_0^1\left(x^{21}+x^{14}+x^7\right)\left(2 x^{14}+3 x^7+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m / n}$ where $l, m , n \in N , m$ and $n$ are coprime then $l+m+n$ is equal to $...........$.

A man is known to speak the truth $3$ out of $4$ times. He throws a die and reports that it is a six. The probability that it is actually a six, is

If $xe^{xy}=y+e^{\sin 2x} ,$ then at $x=0, \, \frac{dy}{dx}$ is equal to -

If $\begin{gathered} f(x)\, = \,\left\{ \begin{gathered}
x\left( {\frac{{{e^{1/x}} - {e^{ - 1/x}}}}{{{e^{1/x}} + {e^{ - 1/x}}}}} \right)\,,\,\,x \ne 0 \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,x\, = \,0\,\,\,\,\,\,\,\,\,\,\,\,\, \hfill \\
\end{gathered} \right. \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ \hfill \\
\end{gathered}$ then correct statement is

If $y = {(x\log x)^{\log \,\log x}}$, then ${{dy} \over {dx}} = $

If $y = {\cos ^{ - 1}}\left( {{{3\cos x + 4\sin x} \over 5}} \right)$, then ${{dy} \over {dx}} = $

If $p, q, r$ are $3$ real numbers satisfying the matrix equation, $[p\,q\,r]\,\left[ {\begin{array}{*{20}{c}}
3&4&1\\
3&2&3\\
2&0&2
\end{array}} \right] = [3\,\,\,0\,\,\,1]$ then $2p + q - r$ equals

The matrix $A = \frac{1}{3}\left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ - 2}\\{ - 2}&2&{ - 1}\end{array}} \right]$is

The value of $\int_\pi ^{2\pi } {[2\sin x]\,dx,} $ where $[\,\,.\,\,]$ represents the greatest integer function, is