x x*log(10*x) + 2
d / x\ --\x*log(10*x) + 2 / dx
Differentiate term by term:
Apply the product rule:
; to find :
Apply the power rule: goes to
; 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:
The result is:
Now simplify:
The answer is:
x 1 + 2 *log(2) + log(10*x)
1 x 2 - + 2 *log (2) x
1 x 3 - -- + 2 *log (2) 2 x