________________ / 2 \/ x - 12*x + 56
/ ________________\ d | / 2 | --\\/ x - 12*x + 56 / dx
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Apply the power rule: goes to
The derivative of a constant times a function is the constant times the derivative of the function.
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:
So, 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:
-6 + x ------------------- ________________ / 2 \/ x - 12*x + 56
2 (-6 + x) 1 - -------------- 2 56 + x - 12*x ------------------- ________________ / 2 \/ 56 + x - 12*x
/ 2 \ | (-6 + x) | 3*|-1 + --------------|*(-6 + x) | 2 | \ 56 + x - 12*x/ -------------------------------- 3/2 / 2 \ \56 + x - 12*x/