If y-cos 2 x- then d y-d x-A- -sin 2 xB- 2 cos xC- none of theseD- sin 2 x

The correct option is A sin 2x y=(cosx)^2 cosx = u ......(1) du dx= sinx ......(2) y=u^2 dy dx=dy du×du dx =(2u)× ( sinx) =(2cosx)( sinx) = sin2x (∵ sin 2x ...

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Byju's Answer

Standard XII

Physics

Double Differentiation

If y=cos 2 x,...

Question

If $y = c o s^{2} x, t h e n \frac{d y}{d x} = ?$

sin 2x

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- sin 2x

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2 cos x

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none of these

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Solution

The correct option is B
- sin 2x

$y = (c o s x)^{2}$
cosx = u ......(1)
$\frac{d u}{d x} = - s i n x$ ......(2)
$y = u^{2}$
$\frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x}$
=(2u) $\times$ (-sinx)
=(2cosx)(-sinx)
=-sin2x ( $∵$ sin 2x=2sinx cosx )

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If y=cos2x, then dydx=?

The correct option is B - sin 2x y=(cosx)2 cosx = u ......(1) dudx=−sinx ......(2) y=u2 dydx=dydu×dudx =(2u)× (-sinx) =(2cosx)(-sinx) =-sin2x (∵ sin 2x=2sinx cosx )

If $y = c o s^{2} x, t h e n \frac{d y}{d x} = ?$

The correct option is B
- sin 2x

$y = (c o s x)^{2}$
cosx = u ......(1)
$\frac{d u}{d x} = - s i n x$ ......(2)
$y = u^{2}$
$\frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x}$
=(2u) $\times$ (-sinx)
=(2cosx)(-sinx)
=-sin2x ( $∵$ sin 2x=2sinx cosx )