Derivative Product, Quotient and Chain Rule

Question

Use the product rule to find the derivative of

(−3x power of 4+4x8)(6e power of x+8)

Use e^x for You do not need to expand out your answer.

Answer 1

Note that the derivative of the exponential function

Dx (f(x))^(g(x)) = f(x) (f(x))^(g(x)) * g'(x)

y = (-3x)^(4+4x^8) * (6e)^(x+8)

Derivative of first times second + derivative of second times first

(-3x) (-3x)^(4+4x^8) (32x^7) * (6e)^(x+8) + (6e) (6e)^(x+8) * (-3x)^(4+4x^8)