/ 2 \ log\2*x - 3*x + 6/
log(2*x^2 - 3*x + 6)
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
Differentiate term by term:
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.
Apply the power rule: goes to
So, the result is:
The result is:
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
-3 + 4*x -------------- 2 2*x - 3*x + 6
2 (-3 + 4*x) 4 - -------------- 2 6 - 3*x + 2*x ------------------ 2 6 - 3*x + 2*x
/ 2 \ | (-3 + 4*x) | 2*|-6 + --------------|*(-3 + 4*x) | 2| \ 6 - 3*x + 2*x / ---------------------------------- 2 / 2\ \6 - 3*x + 2*x /
/ 2 \ | (-3 + 4*x) | 2*|-6 + --------------|*(-3 + 4*x) | 2| \ 6 - 3*x + 2*x / ---------------------------------- 2 / 2\ \6 - 3*x + 2*x /