3 2 (2*x - 1) *(x + 2)
d / 3 2\ --\(2*x - 1) *(x + 2) / dx
Apply the product rule:
; to find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
; 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 (2*x - 1) *(4 + 2*x) + 6*(x + 2) *(2*x - 1)
/ 2 2 \ 2*(-1 + 2*x)*\(-1 + 2*x) + 12*(2 + x) + 12*(-1 + 2*x)*(2 + x)/
/ 2 2 \ 12*\3*(-1 + 2*x) + 4*(2 + x) + 12*(-1 + 2*x)*(2 + x)/