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
If $y = \sin (\sqrt {\sin x + \cos x} )$, then ${{dy} \over {dx}} = $
  • A
    ${1 \over 2}{{\cos \sqrt {\sin x + \cos x} } \over {\sqrt {\sin x + \cos x} }}$
  • B
    ${{\cos \sqrt {\sin x + \cos x} } \over {\sqrt {\sin x + \cos x} }}$
  • ✓
    ${1 \over 2}{{\cos \sqrt {\sin x + \cos x} } \over {\sqrt {\sin x + \cos x} }}.(\cos x - \sin x)$
  • D
    None of these
✓

Answer

Correct option: C.
${1 \over 2}{{\cos \sqrt {\sin x + \cos x} } \over {\sqrt {\sin x + \cos x} }}.(\cos x - \sin x)$
c
(c) $y = \sin (\sqrt {\sin x + \cos x} )$

$\frac{{dy}}{{dx}} = \frac{1}{2}\frac{{\cos (\sqrt {\sin x + \cos x} )}}{{\sqrt {\sin x + \cos x} }}(\cos x - \sin x)$.

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

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

Similar questions

Any circle through the points of intersection of the lines $x + \sqrt 3\, y = 1$ and $\sqrt 3\, x -y = 2$ if intersects these lines at points $P$ and $Q$, then the angle subtended by the arc $PQ$ at its centre is- ............. $^o$
→
Let $A =\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & -2 \\ 0 & 1\end{array}\right]$ and $P =\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right], \theta>0$.
If $B = PAP ^{ T }, C = P ^{\top} B ^{10} P$ and the sum of the diagonal elements of C is $\frac{ m }{ n }$, where $\operatorname{gcd}( m , n )=$ 1 , then $m + n$ is :
→
Let $2^{\text {nd }}, 8^{\text {th }}$ and $44^{\text {th }}$, terms of a non$-$constant $A.P.$ be respectively the $1^{\text {st }}, 2^{\text {nd }}$ and $3^{\text {rd }}$ terms of $G.P.$ If the first term of $A.P.$ is $1$ then the sum of first $20$ terms is equal to$-$
→
Area of the greatest rectangle that can be inscribed in the ellipse ${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$ is
→
The area bounded by the curve $y = f(x)$ , the co-ordinate axes $\&$ the line $x = x_1$ is given by $x_1 \cdot {e^{{x_1}}}$. Therefore $f (x)$ equals:
→
$\int {\sqrt {\frac{{1 + x}}{{1 - x}}} \,\,dx = } $
→
$\frac{2^{3}-1^{3}}{1 \times 7}+\frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 \times 11}+$$\frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 \times 15}+\ldots .+$ $\frac{30^{3}-29^{3}+28^{3}-27^{3}+\ldots+2^{3}-1^{3}}{15 \times 63}$is equal to.
→
The coefficients $\mathrm{a}, \mathrm{b}, \mathrm{c}$ in the quadratic equation $a x^2+b x+c=0$ are chosen from the set $\{1,2,3,4,5,6,7,8\}$. The probability of this equation having repeated roots is :
→
If centre of a regular hexagon is at origin and one of the vertex on argand diagram is $1 + 2i$, then its perimeter is
→
Let the equation of two sides of a triangle be $3x\,-\,2y\,+\,6\,=\,0$ and $4x\,+\,5y\,-\,20\,=\,0.$ If the orthocentre of this triangle is at $(1, 1),$ then the equation of its third side is
→