___ 3 3*\/ x + log (x)
d / ___ 3 \ --\3*\/ x + log (x)/ dx
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:
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:
The result is:
The answer is:
2 3 3*log (x) ------- + --------- ___ x 2*\/ x
/ 2 \ | 1 log (x) 2*log(x)| 3*|- ------ - ------- + --------| | 3/2 2 2 | \ 4*x x x /
/ 2 \ |2 3 6*log(x) 2*log (x)| 3*|-- + ------ - -------- + ---------| | 3 5/2 3 3 | \x 8*x x x /