Question

Find the derivative of the following function showing your work and fully simplifying your answer. Show steps please! Thank you!!!!!!

f(x)=(x+3)^3(x-8)^5

Answer 1

I got up to here.

f'(x)= 3(x+3)^2(x8)^5(d/dx(x))+5(x+3)^3(x-8)^4

Answer 2

d/dx(x) = dx/dx = 1
So, how come you included it in d/dx (x+3) but not in d/dx (x-8)?
Your work so far is correct.

3(x+3)^2(x-8)^5(d/dx(x))+5(x+3)^3(x-8)^4
3(x+3)^2(x-8)^5 + 5(x+3)^3(x-8)^4
Now factor out some stuff:

(x+3)^2 (x-8)^4 (3(x-8)+5(x+3))
(x+3)^2 (x-8)^4 (8x-9)