2 (x + 3) *(x + 5) - 1
(x + 3)^2*(x + 5) - 1
Differentiate term by term:
Apply the product rule:
; 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:
; to find :
Differentiate term by term:
Apply the power rule: goes to
The derivative of the constant is zero.
The result is:
The result is:
The derivative of the constant is zero.
The result is:
Now simplify:
The answer is:
2 (x + 3) + (6 + 2*x)*(x + 5)