Please help, I am stuck...

Question

Find F ′(x) for .

Options:

1)	sin(24) - sin(x12)
2)	sin(x7)
3)	-sin(x12)
4)	-3x2sin(x12)

Answer 1

We apply Leibniz' integral rule:

F'(x) = sin(2^4)*d/dx(2) - sin((x^3)^4)*d/dx(x^3)

= sin(2^4)*0 - sin(x^12)*3x^2

= -3x^2sin(x^12).