How do you differentiate #f(x)= e^x/(e^(3-x) -x )# using the quotient rule?

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Answer 1 · 2018-05-07T15:11:03

Just apply the quotient rule.

If you think about it, you basically have:

#f(x)=(h(x))/g(x)#

as such, we can apply our quotient rule:

#f'(x)=(h'(x)g(x)-h(x)g'(x))/(g(x))^2#

and then get this:

#f'(x)=((e^x)(e^(3-x)-x)-(e^x)(-e^(3-x)-1))/(e^(3-x)-x)^2#

And I'll leave the simplifying to you :)