Download App

STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
${d \over {dx}}{\sin ^{ - 1}}(2ax\sqrt {1 - {a^2}{x^2}} ) = $
  • A
    ${{2a} \over {\sqrt {{a^2} - {x^2}} }}$
  • B
    ${a \over {\sqrt {{a^2} - {x^2}} }}$
  • ✓
    ${{2a} \over {\sqrt {1 - {a^2}{x^2}} }}$
  • D
    ${a \over {\sqrt {1 - {a^2}{x^2}} }}$
✓

Answer

Correct option: C.
${{2a} \over {\sqrt {1 - {a^2}{x^2}} }}$
c
(c) $\frac{d}{{dx}}{\sin ^{ - 1}}(2ax\sqrt {1 - {a^2}{x^2}} )$

Putting $ax = \sin \theta ,$ we get

$ = \frac{d}{{dx}}{\sin ^{ - 1}}[2\sin \theta \sqrt {1 - {{\sin }^2}\theta } ] = \frac{d}{{dx}}{\sin ^{ - 1}}\sin 2\theta = \frac{{2a}}{{\sqrt {1 - {a^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

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

Similar questions

If four distinct points with position vectors $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$ are coplanar; then $[\vec{a} \vec{b} \vec{c}]$ is equal to
→
If $f(x) = ax + b$ and $g(x) = cx + d$, then $f(g(x)) = g(f(x))$ is equivalent to
→
Let $f(x)=\left|\begin{array}{ccc}a & -1 & 0 \\ a x & a & -1 \\ a x^{2} & a x & a\end{array}\right|, a \in R$. Then the sum of which the squares of all the values of a for $2 f^{\prime}(10)-f^{\prime}(5)+100=0$ is
→
If $\sin 6\theta = 32{\cos ^5}\theta \sin \theta - 32{\cos ^3}\theta \sin \theta + 3x,$ then $x = $
→
If ${y_1},\;{y_2}$ are the ordinates of two points $P$ and $Q$ on the parabola and ${y_3}$ is the ordinate of the point of intersection of tangents at $P$ and $Q$, then
→
Let $A =\{2,3,6,8,9,11\}$ and $B =\{1,4,5,10,15\}$ Let $R$ be a relation on $A \times B$ define by $( a , b ) R ( c , d )$ if and only if $3 ad -7 bc$ is an even integer. Then the relation $R$ is
→
Let $A=\{n \in N: H . C . F .(n, 45)=1\}$ and Let $B=\{2 k: k \in\{1,2, \ldots, 100\}\}$. Then the sum of all the elements of $A \cap B$ is
→
Let $P Q$ be a chord of the parabola $y^2=12 x$ and the midpoint of $PQ$ be at $(4,1)$. Then, which of the following point lies on the line passing through the points $\mathrm{P}$ and $\mathrm{Q}$ ?
→
If an antiderivative of $f(x)$ is ${e^x}$ and that of $g(x)$ is $\cos x,$then $\int {f(x)\cos x\,dx} + \int {g(x){e^x}dx = } $
→
Let $\alpha, \beta, \gamma$ and $\delta$ be the coefficients of $x^7, x^5, x^3$ and $x$ respectively in the expansion of $\left(x+\sqrt{x^3-1}\right)^5+\left(x-\sqrt{x^3-1}\right)^5, x>1$. If $u$ and $v$ satisfy the equations
$
\begin{array}{l}
\alpha u+\beta v=18, \\
\gamma u+\delta v=20,
\end{array}
$
then $u+v$ equals :
→