d dy ( ^ - 1 ( 3y 2 - y^3 2 ) ) = - Vidyadip

MCQ

$\frac{d}{{dy}}\left( {{{\sin }^{ - 1}}\left( {\frac{{3y}}{2} - \frac{{{y^3}}}{2}} \right)} \right) = $

✓
$\frac{3}{{\sqrt {4 - {y^2}} }}$
B
$\frac{-3}{{\sqrt {4 - {y^2}} }}$
C
$\frac{1}{{\sqrt {4 - {y^2}} }}$
D
$\frac{-1}{{\sqrt {4 - {y^2}} }}$

✓

Answer

Correct option: A.

$\frac{3}{{\sqrt {4 - {y^2}} }}$

a
$ P =\sin^{ -1}\left(3\left(\frac{y}{2}\right)-4\left(\frac{4}{2}\right)^{3}\right) $

Put $ \quad \frac{y}{2} =\sin \theta $

$ P =\sin ^{-1}(\sin 3 \theta)=3 \theta$

$ P =3 \sin ^{-1} \frac{y}{2} $

$ \frac{d P}{d y} =\frac{3}{\sqrt{4-y^{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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $P=\left[\begin{array}{ccc}1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 & 4 & 1\end{array}\right]$ and $I$ be the identity matrix of order $3$ . If $\left.Q=q_{i j}\right]$ is a matrix such that $P^{50}-Q=I$, then $\frac{q_{31}+q_{32}}{q_{21}}$ equals

If z is a complex number, then the number of common roots of the equation $z^{1985}+z^{100}+1=0$ and $z^3+2 z^2+2 z+1=0$, is equal to :

If $a,\,b,\,c$ are non-coplanar vectors and $d = \lambda a + \mu \,b + \nu c,$ then $\lambda $ is equal to

If the foci of an ellipse are $( \pm \sqrt 5 ,\,0)$ and its eccentricity is $\frac{{\sqrt 5 }}{3}$, then the equation of the ellipse is

How many words can be made from the letters of the word $BHARAT$ in which $ B $ and $H$ never come together

Let $S$ be the set of all triangle in the $xy -$ plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in $S$ has area $50$ sq. units, then the number of elements in the set $S$ is

Let $\left(1+x+x^2\right)^{2014}=a_0+a_1 x+a_2 x^2+a_3 x^3$

$+\ldots+a_{4028} x^{4028}$ and let $A=a_0-a_3+a_6-\ldots+a_{4026}$,

$B=a_1-a_4+a_7-\ldots-a_{4027}$

$C=a_2-a_5+a_8-\ldots+a_{4028}$ Then,

Let $S_n$ be the sum to n-terms of an arithmetic progression $3,7,11, \ldots \ldots$. . If $40<\left(\frac{6}{\mathrm{n}(\mathrm{n}+1)} \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{S}_{\mathrm{k}}\right)<42$, then $\mathrm{n}$ equals

The value of $\int_0^{2\pi } {|{{\sin }^3}\theta |\,d\theta } $ is

The image of the point $(4, \,-3)$ with respect to the line $y = x$ is