What is the d/(dt)((e^t)/(4-3e^t)) ?

The d/(dt)((e^t)/(4-3e^t)) is (4e^t)/((4-3e^t)^2)

What is the first d/(dt)((e^t)/(4-3e^t)) ?

The first d/(dt)((e^t)/(4-3e^t)) is (4e^t)/((4-3e^t)^2)

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\frac{d}{d t} (\frac{e ^{t}}{4 - 3 e ^{t}})

\frac{4 e ^{t}}{( 4 - 3 e ^{t} ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{e ^{t}}{4 - 3 e ^{t}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d t} ( e ^{t} ) ( 4 - 3 e ^{t} ) - \frac{d}{d t} ( 4 - 3 e ^{t} ) e ^{t}}{( 4 - 3 e ^{t} ) ^{2}}

\frac{d}{d t} (e^{t}) = e^{t}

\frac{d}{d t} (4 - 3 e^{t}) = - 3 e^{t}

= \frac{e ^{t} ( 4 - 3 e ^{t} ) - ( - 3 e ^{t} ) e ^{t}}{( 4 - 3 e ^{t} ) ^{2}}

Simplify

\frac{e ^{t} ( 4 - 3 e ^{t} ) - ( - 3 e ^{t} ) e ^{t}}{( 4 - 3 e ^{t} ) ^{2}} : \frac{4 e ^{t}}{( 4 - 3 e ^{t} ) ^{2}}

= \frac{4 e ^{t}}{( 4 - 3 e ^{t} ) ^{2}}

n = 0 \sum \infty \frac{n}{2 ^{n}} x^{n}

\int_{0}^{1} 1 - x d x

\frac{\partial}{\partial x} (x y w)

\frac{d}{d x} (cos (2 y) - 3 x^{2} y^{2})

\int x (x^{2} + 5)^{3} d x

What is the d/(dt)((e^t)/(4-3e^t)) ?
The d/(dt)((e^t)/(4-3e^t)) is (4e^t)/((4-3e^t)^2)
What is the first d/(dt)((e^t)/(4-3e^t)) ?
The first d/(dt)((e^t)/(4-3e^t)) is (4e^t)/((4-3e^t)^2)