Question

differentiate:

y= (ae^{x} + b)/(ce^{x} + d)

Answer 1

\[y=\frac{ ae ^{x} + b }{ ce ^{x} +d } \]

Answer 2

f(x) = ae^x + b, then f'(x) = ae^x

g(x) = ce^x + d, then g'(x) = ce^x

You have y = f(x)/g(x)

The derivative of this is

(f'(x)*g(x) - g'(x)*f(x))/g(x)^2

So

((ae^x)(ce^x + d) - (ce^x)(ae^x + b))/(ce^x)^2

Answer 3

Hmmm that's what I got but it says the answer is:

\[\frac{ (ad-bc)e ^{x} }{ (ce ^{x}+d)^{2} }\]

Answer 4

if you multiply everything on the top out, you get

ace^(2x) + ade^x - ace^(2x) - bce^x ===> ade^x - bce^x ==> (ad-bc)e^x

I also mistyped something in my earlier answer, it should be (ce^x +d)^2 on the bottom. Sorry about that.