How do you find the second derivative of y=sinxcosx?

Answer 1

y' = cos^2x - sin^2x
y'' = - 2sinxcosx - 2sinxcosx
y'' = - 4sinxcosx

Answer 2

Use the product rule to find the derivative. Then take the derivative again.

Answer 3

y = sinxcosx
hence y = 1/2(sin2x) (double angle formula)

thus, y' = cos2x (derivative of sin is cos)

thus, y'' = -2sin2x (Derivative of cos is -sin)

Answer 4

One way is to apply the sine double angle formula sin(2x) = 2 sin x cos x, therefore y = sin(2x)/2

y' = cos(2x)*2/2 = cos (2x)
y'' = - 2 sin(2x).