_______________ / 2 \/ 27 + 6*x - x
/ _______________\ d | / 2 | --\\/ 27 + 6*x - x / dx
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of the constant is zero.
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 result of the chain rule is:
Now simplify:
The answer is:
3 - x ------------------ _______________ / 2 \/ 27 + 6*x - x
/ 2 \ | (-3 + x) | -|1 + -------------| | 2 | \ 27 - x + 6*x/ --------------------- _______________ / 2 \/ 27 - x + 6*x
/ 2 \ | (-3 + x) | -3*|1 + -------------|*(-3 + x) | 2 | \ 27 - x + 6*x/ ------------------------------- 3/2 / 2 \ \27 - x + 6*x/