3 2 x *(x + 2)
d / 3 2\ --\x *(x + 2) / dx
Apply the product rule:
; to find :
Apply the power rule: goes to
; to find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Apply the power rule: goes to
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
3 2 2 x *(4 + 2*x) + 3*x *(x + 2)
/ 2 2 \ 2*x*\x + 3*(2 + x) + 6*x*(2 + x)/
/ 2 2 \ 6*\(2 + x) + 3*x + 6*x*(2 + x)/