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 result is:
The result of the chain rule is:
Now simplify:
The answer is:
3 / 2 \ \6*x + 7*x/ *(28 + 48*x)
2 2 / 2 \ 12*x *(7 + 6*x) *\(7 + 12*x) + 4*x*(7 + 6*x)/
/ 2 \ 24*x*(7 + 6*x)*(7 + 12*x)*\(7 + 12*x) + 18*x*(7 + 6*x)/