Download App

5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $y = {(\cos {x^2})^2}$ then ${{dy} \over {dx}}$ is equal to
  • A
    $ - 4x\sin 2{x^2}$
  • B
    $ - x\sin {x^2}$
  • ✓
    $ - 2x\sin 2{x^2}$
  • D
    $ - x\cos 2{x^2}$
✓

Answer

Correct option: C.
$ - 2x\sin 2{x^2}$
c
(c) $y = {(\cos {x^2})^2}$;   $\frac{{dy}}{{dx}} = 2\cos {x^2}.( - \sin {x^2}).2x$

$\frac{{dy}}{{dx}} = - 4x\sin {x^2}\cos {x^2} = - 2x\sin 2{x^2}$.

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

If $\tan^{-1}\frac{\text{x}+1}{\text{x}-1}+\tan^{-1}\frac{\text{x}-1}{\text{x}}=\tan^{-1}(-7),$ then the value of x is:
  1. 0
  2. -2
  3. 1
  4. 2
→
Let $C_{1}$ be the curve obtained by the solution of differential equation $2 xy \frac{ dy }{ dx }= y ^{2}- x ^{2}, x > 0$ Let the curve $C _{2}$ be the solution of $\frac{2 x y}{x^{2}-y^{2}}=\frac{d y}{d x} .$ If both the curves pass through $(1,1),$ then the area enclosed by the curves $C_{1}$ and $C _{2}$ is equal to :
→
The function $f(x)=x+\frac{4}{x}$ has
→
If a line makes angle $\alpha,\beta$ and $\gamma$ with the axes respectively, then $\cos2\alpha+\cos2\beta+\cos2\gamma=$
  1. -2
  2. -1
  3. 1
  4. 2
→
The value of the integral $\int\limits_{-2}^{2} \frac{\left|x^{3}+x\right|}{\left(e^{x|x|}+1\right)} d x$ is equal to
→
If $y = {{{e^{2x}}\cos x} \over {x\sin x}},$ then ${{dy} \over {dx}} = $
→
Let $A$ be a non-zero periodic matrix with period $4$ and $A^{12} + B =I$, where $I$ is identity matrix and $B$ is any square matrix of same order as of $A$. Matrix product $AB$ is equal to
→
Let $a, b, c, d$ be in arithmetic progression with common difference $\lambda$. If

$\left|\begin{array}{lll} x+a-c & x+b & x+a \\ x-1 & x+c & x+b \\ x-b+d & x+d & x+c \end{array}\right|=2$

then value of $\lambda^{2}$ is equal to $.....$

→
A vector whose initial and terminal points coincide, is:
  1. Zero Vector
  2. Equal Vectors
  3. Null Vector
  4. Unit Vector
→
$\int \limits_{6}^{16} \frac{\log _{\mathrm{e}} x^{2}}{\log _{e} x^{2}+\log _{e}\left(x^{2}-44 x+484\right)} d x$ is equal to:
→