If f(x)=(x^3−2x)^5 , find f'(x).
f(x)=(x3-2x)5
If we look at this function, we can see that it can be split into two functions, one hiding in the other one. Because of that, to solve this problem we will need the Chain rule:
f(g(x))' = f'(g(x)) . g'(x)
If we apply this formula, we can see that f(g(x)) = (x3-2x)5 and that g(x) = x3-2x .
The derivative of (x3-2x)5 is 5(x3-2x)4 And the derivative of x3-2x is 3x2 - 2
If we plug the results back into the chain rule formula, we get the result:
f'(x) = 5(x3-2x)4 . (3x2 - 2)
