3 3*x - log (x + 3)
d / 3 \ --\3*x - log (x + 3)/ 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:
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Apply the power rule: goes to
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
The result of the chain rule is:
So, the result is:
The result is:
Now simplify:
The answer is:
2 3*log (x + 3) 3 - ------------- x + 3
3*(-2 + log(3 + x))*log(3 + x) ------------------------------ 2 (3 + x)
/ 2 \ 6*\-1 - log (3 + x) + 3*log(3 + x)/ ----------------------------------- 3 (3 + x)