D - dx -3sin2 x -3-cos2 x -3-A- 4 cos 2 x- -4 sin 2 x- 4 sin 2 xD- -4 cos 2 x

The correct option is B 4sin 2xddx[√(3)sin(2x+π3)+cos(2x+π3)] = ddx[2√(3)2sin(2x+π3)+22cos(2x+π3)] = ddx2[sin(2x+π3)cosπ6+cos(2x+π3)sinπ6] = ddx2[sin(2x+π3+π6 ...

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Byju's Answer

Standard XII

Mathematics

Implicit Differentiation

d / dx [√3sin...

Question

$\frac{d}{d x} [\sqrt{3} sin (2 x + \frac{π}{3}) + cos (2 x + \frac{π}{3})] =$ ____

4 cos 2 x

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- 4 sin 2 x

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4 sin 2 x

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- 4 cos 2 x

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Solution

The correct option is B $- 4 sin 2 x$
$\frac{d}{d x} [\sqrt{3} sin (2 x + \frac{π}{3}) + cos (2 x + \frac{π}{3})]$
$= \frac{d}{d x} [\frac{2 \sqrt{3}}{2} sin (2 x + \frac{π}{3}) + \frac{2}{2} cos (2 x + \frac{π}{3})]$
$= \frac{d}{d x} 2 [sin (2 x + \frac{π}{3}) cos \frac{π}{6} + cos (2 x + \frac{π}{3}) sin \frac{π}{6}]$
$= \frac{d}{d x} 2 [sin (2 x + \frac{π}{3} + \frac{π}{6})]$
$= \frac{d}{d x} 2 [sin (2 x + \frac{π}{2})]$
$= \frac{d}{d x} (2 cos 2 x)$
$= - 4 sin 2 x$

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Similar questions

\frac{d}{d x} (\sqrt{3} sin (2 x + \frac{π}{3}) + cos (2 x + \frac{π}{3})) =

_________.

Q. If

\frac{d y}{d x} + \frac{3}{{c o s}^{2} x} = \frac{1}{{c o s}^{2} x}, x ϵ (\frac{- π}{3}, \frac{π}{3}),

and

y (\frac{π}{4}) = \frac{4}{3},

then

y (- \frac{π}{4})

equals:

Q. If

f (x) = {cos}^{2} x + {cos}^{2} (x + \frac{π}{3}) + sin x sin (x + \frac{π}{3})

and

g (\frac{5}{4}) = 3

, then

\frac{d}{d x} (g o f (x))

Q. Prove

{cos}^{2} x + {cos}^{2} (x + \frac{π}{3}) + {cos}^{2} (x - \frac{π}{3}) = \frac{3}{2}

Q. Prove that

{cos}^{2} x + {cos}^{2} (x + \frac{π}{3}) + {cos}^{2} (x - \frac{π}{3}) = \frac{3}{2}

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ddx[√3sin(2x+π3)+cos(2x+π3)]=____

The correct option is B −4sin2xddx[√3sin(2x+π3)+cos(2x+π3)] =ddx[2√32sin(2x+π3)+22cos(2x+π3)] =ddx2[sin(2x+π3)cosπ6+cos(2x+π3)sinπ6] =ddx2[sin(2x+π3+π6)] =ddx2[sin(2x+π2)] =ddx(2cos2x) =−4sin2x

$\frac{d}{d x} [\sqrt{3} sin (2 x + \frac{π}{3}) + cos (2 x + \frac{π}{3})] =$ ____