How do you differentiate f(x)=e^(x-(x-2)^2 using the chain rule.?

1 Answer
Jan 18, 2017

f'(x) = (5 - 2x)e^(-x^2 + 5x - 4)

Explanation:

Expand:

f(x) = e^(x - (x^2 - 4x + 4))

f(x) = e^(x - x^2 + 4x - 4)

f(x) = e^(-x^2 + 5x - 4)

We now use the chain rule to differentiate. Let y = e^u and u = -x^2 + 5x - 4. Then y' = e^u and u' = -2x + 5.

f'(x) = u' * y'

f'(x) = e^u * 2x + 5

f'(x) = (5 - 2x)e^(-x^2 + 5x - 4)

Hopefully this helps!