_______________ / 2 \/ x - 6*x - 11
/ _______________\ d | / 2 | --\\/ x - 6*x - 11 / 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:
-3 + x ------------------ _______________ / 2 \/ x - 6*x - 11
2 (-3 + x) 1 - -------------- 2 -11 + x - 6*x ------------------- ________________ / 2 \/ -11 + x - 6*x
/ 2 \ | (-3 + x) | 3*|-1 + --------------|*(-3 + x) | 2 | \ -11 + x - 6*x/ -------------------------------- 3/2 / 2 \ \-11 + x - 6*x/