what is the derivative of (x^2)(cos[x^3])?

Question

what is the derivative of (x^2)(cos[x^3])?

Answer 1

x^2(-sinx^3)(3x^2)+2xcosx^3
=-3x^4sinx^3+2xcosx^3
use chain rule, product rule

Answer 2

first, use the product rule:

d/dx [x^2 cos[x^3]] = x^2 d/dxcos[x^3] + cos[x^3] d/dx(x^2)

d/dx (x^2) = 2x

d/dx(cos[x^3]) = -3x^2 sin[x^3]

so the the final derivative is:

-3x^4 sin[x^3] + 2x cos[x^3]

Answer 3

Use product rule
dy/dx = 2xcos(x^3) -3x^2*x^2sin(x^3)
dy/dx = 2xcos(x^3) -3x^4sin(x^3)

Answer 4

using product rule - (uv)'=u'v+v'u
derivative= 2xcos(x^3) +x^2{-sin(x^3)3x^2}
=2xcos(x^3) -x^2{sin(x^3)3x^2}
=2xcos(x^3) -3x^4{sin(x^3)}

Answer 5

2*x*cos(x^3)-3*(x^4)sin(x^3)