6 / 2 \ \x + 4*x - 1/
(x^2 + 4*x - 1)^6
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
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.
Apply the power rule: goes to
So, the result is:
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:
5 / 2 \ \x + 4*x - 1/ *(24 + 12*x)
4 / 2 \ / 2 2\ 12*\-1 + x + 4*x/ *\-1 + x + 4*x + 10*(2 + x) /
3 / 2 \ / 2 2 \ 120*\-1 + x + 4*x/ *(2 + x)*\-3 + 3*x + 8*(2 + x) + 12*x/