Apply the product rule:
; to find :
Let .
The derivative of is itself.
Then, apply the chain rule. Multiply by :
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 result of the chain rule is:
; to find :
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
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 result of the chain rule is:
The result is:
Now simplify:
The answer is:
3*x e 3*x ---- + 3*e *log(8*x) x
/ 1 6 \ 3*x |- -- + - + 9*log(8*x)|*e | 2 x | \ x /
/ 9 2 27 \ 3*x |- -- + -- + -- + 27*log(8*x)|*e | 2 3 x | \ x x /