How do you differentiate f(x) = (e^(4-x))/(e^(1-x)-1) using the quotient rule?

1 Answer
Apr 20, 2017

f'(x) = e^(4-x) / (e^(1-x)-1)^2

Explanation:

f(x)=u/v, f'(x)=(u'v-v'u)/v^2

So, we need u' and v':

u' = (e^(4-x))' = e^(4-x) * (4-x)' = -e^(4-x)

v' = (e^(1-x) - 1)' = e^(1-x) * (1-x)' = -e^(1-x)

f'(x) = (-e^(4-x) * (e^(1-x) - 1) + e^(1-x) * e^(4-x)) / (e^(1-x)-1)^2

f'(x) = (-e^(5-2x) + e^(4-x) + e^(5-2x)) / (e^(1-x)-1)^2

f'(x) = e^(4-x) / (e^(1-x)-1)^2