Chain Rule?

Question

Find the derivative of

f(x)= 8e^x/(e^x)+1

Answer 1

is it (8e^x / e^x) + 1
or 8e^x / (e^x + 1)?

i assume the second one because if you simplify the first expression the answer is 9, and we don't have to use the chain rule

so 8e^x / (e^x + 1)

8 * d/dx [ e^x / (e^x + 1) ]

quotient rule
d/dx (u/v) = (u'v - v'u)/v^2

8 [ d/dx (e^x) (e^x + 1) - d/dx (e^x + 1) (e^x) ] / (e^x + 1)^2

derivative of e^x is e^x
8 [ e^x (e^x + 1) - (e^x)(e^x) ] / (e^x + 1)^2

8 [ e^(2x) + e^x - e^(2x) ] / (e^x + 1)^2

8 (e^x) / (e^x + 1)^2

8e^x / (e^x + 1)^2