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bettyboop8904
 2 years ago
differentiate:
y= (ae^{x} + b)/(ce^{x} + d)
bettyboop8904
 2 years ago
differentiate: y= (ae^{x} + b)/(ce^{x} + d)

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bettyboop8904
 2 years ago
Best ResponseYou've already chosen the best response.0\[y=\frac{ ae ^{x} + b }{ ce ^{x} +d } \]

CanadianAsian
 2 years ago
Best ResponseYou've already chosen the best response.1f(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

bettyboop8904
 2 years ago
Best ResponseYou've already chosen the best response.0Hmmm that's what I got but it says the answer is: \[\frac{ (adbc)e ^{x} }{ (ce ^{x}+d)^{2} }\]

CanadianAsian
 2 years ago
Best ResponseYou've already chosen the best response.1if you multiply everything on the top out, you get ace^(2x) + ade^x  ace^(2x)  bce^x ===> ade^x  bce^x ==> (adbc)e^x I also mistyped something in my earlier answer, it should be (ce^x +d)^2 on the bottom. Sorry about that.
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