4 log(5*x) + 3*x
d / 4\ --\log(5*x) + 3*x / dx
Differentiate term by term:
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 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 is:
Now simplify:
The answer is:
/1 \ 2*|-- + 36*x| | 3 | \x /