Question

How do I use the quotient rule to simplify (find the derivatives of): f(x)=e^2x/x^4

Answer 1

ok quotient rule is--
\[D[ \frac{ f(x) }{ g(x) }]=\frac{ g(x).f'(x)-f(x).g'(x) }{ g(x)^2 }\]
@StudyMom74

Answer 2

given here
\[F=\frac{ e^{2x} }{ x^4 }\\so ~here~~\\f(x)=e^{2x}\\g(x)=x^4\]

Answer 3

f(x) will be derived by the chain rule (don't forget).

\(\large\color{black}{ \frac{d}{dx}( e^{2x} ) =e^{2x}~\times \frac{d}{dx}( 2x ) =e^{2x}\times 2=2e^{2x}}\)

g(x) is just derived by the power rule...

go for it.