/ 2 \ log\3*x - 5/ ------------- log(5)
/ / 2 \\ d |log\3*x - 5/| --|-------------| dx\ log(5) /
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
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:
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
So, the result is:
Now simplify:
The answer is:
6*x ----------------- / 2 \ \3*x - 5/*log(5)
/ 2 \ | 6*x | -6*|-1 + ---------| | 2| \ -5 + 3*x / ------------------- / 2\ \-5 + 3*x /*log(5)
/ 2 \ | 4*x | 108*x*|-1 + ---------| | 2| \ -5 + 3*x / ---------------------- 2 / 2\ \-5 + 3*x / *log(5)