Question

Given y = sin2x, then find
dv/dx

1)2sin power 2x
2)2cosx
3) 2cos2x
4)COS2X/2

Answer 1

Answer:

I think its answer 3)2cos2x

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Given y = sin 2x then

$\displaystyle \sf{ \frac{dy}{dx} } =$

$\displaystyle \sf{ 1) \: \: 2 { \sin}^{2} x }$

$\displaystyle \sf{ 2) \: \:2 \cos x }$

$\displaystyle \sf{ 3) \: \: 2 \cos 2x }$

$\displaystyle \sf{4) \: \: \: \frac{ \cos 2x}{2} }$

EVALUATION

Here it is given that

y = sin 2x

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{dy}{dx} = \frac{d}{dx} \bigg( \sin 2x \bigg)}$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} = \cos 2x \frac{d}{dx} \bigg( 2x \bigg)}$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} =2 \cos 2x }$

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf{ 3) \: \: 2 \cos 2x }$

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