___________________ / 2 \/ 14*x + 16*x + 23
/ ___________________\ d | / 2 | --\\/ 14*x + 16*x + 23 / dx
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
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 derivative of the constant is zero.
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
8 + 14*x ---------------------- ___________________ / 2 \/ 14*x + 16*x + 23
/ 2 \ | 2*(4 + 7*x) | 2*|7 - -----------------| | 2 | \ 23 + 14*x + 16*x/ ------------------------- ___________________ / 2 \/ 23 + 14*x + 16*x
/ 2 \ | 2*(4 + 7*x) | 12*|-7 + -----------------|*(4 + 7*x) | 2 | \ 23 + 14*x + 16*x/ ------------------------------------- 3/2 / 2 \ \23 + 14*x + 16*x/