Question

If y=sin x+cos 2x, then
d²y/dx² is

(1) sin x +4sin 2x
(2) sin x + 4 cos 2x
(3) - [sin x +4cos 2x]
(4) sin x +cos2x/4
i need step explanation pls ans it
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Answer 1

Answer:

(3)-[sinx+4cos2x]

Explanation:

Given y=sinx+cos2x

dy/dx=cosx-2sin2x

d²y/dx²=(-sinx-4cos2x)

d²y/dx²=-[sinx+4cos2x]

Answer 2

Explanation:

y=sinx+cos2x

differentiate with respect to x,

dy/dx=d/dx(sinx)+d/dx(cos2x). =cosx+(-sin2x)d/dx(2x)

dy/dx =cosx+2(-sin2x)

again differentiate with respect to x,.

d^2y/dx^2=d/dx(cosx)+2d/dx(-sin2x)

=(-sinx)+2*(-cos2x)*d/dx(2x)

=-sinx-4cos2x

= -(sinx+4cos2x)