x e *log(5*x)
d / x \ --\e *log(5*x)/ dx
Apply the product rule:
; to find :
The derivative of is itself.
; 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:
x e x -- + e *log(5*x) x
/ 1 2 \ x |- -- + - + log(5*x)|*e | 2 x | \ x /
/ 3 2 3 \ x |- -- + -- + - + log(5*x)|*e | 2 3 x | \ x x /