/ 5\ |/ 3 \ | \\-log (x)/ / e
/ / 5\\ | |/ 3 \ || d | \\-log (x)/ /| --\e / dx
Let .
The derivative of is itself.
Then, apply the chain rule. Multiply by :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of is .
The result of the chain rule is:
So, the result is:
The result of the chain rule is:
The result of the chain rule is:
Now simplify:
The answer is:
/ 5\ |/ 3 \ | 14 \\-log (x)/ / -15*log (x)*e --------------------------- x
/ 5\ |/ 3 \ | 13 / 15 \ \\-log (x)/ / 15*log (x)*\-14 + 15*log (x) + log(x)/*e ------------------------------------------------------- 2 x
/ 5\ |/ 3 \ | 12 / 30 16 2 15 \ \\-log (x)/ / 15*log (x)*\-182 - 225*log (x) - 45*log (x) - 2*log (x) + 42*log(x) + 630*log (x)/*e ----------------------------------------------------------------------------------------------------- 3 x