/ 3\ log\x + x / ----------- log(4)
/ / 3\\ d |log\x + x /| --|-----------| dx\ log(4) /
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:
Apply the power rule: goes to
Apply the power rule: goes to
The result is:
The result of the chain rule is:
So, the result is:
Now simplify:
The answer is:
2 1 + 3*x --------------- / 3\ \x + x /*log(4)
2 / 2\ \1 + 3*x / 6 - ----------- 2 / 2\ x *\1 + x / --------------- / 2\ \1 + x /*log(4)
/ 3 \ | / 2\ / 2\ | | 9*\1 + 3*x / \1 + 3*x / | 2*|3 - ------------ + ------------| | 2 2| | 1 + x 2 / 2\ | \ x *\1 + x / / ----------------------------------- / 2\ x*\1 + x /*log(4)