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

1 Answer
Jan 18, 2017

Answer:

#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!