What is the d/(dt)((e^{2t})/(1-t^2)) ?

The d/(dt)((e^{2t})/(1-t^2)) is (2e^{2t}(1-t^2)+2e^{2t}t)/((1-t^2)^2)

What is the first d/(dt)((e^{2t})/(1-t^2)) ?

The first d/(dt)((e^{2t})/(1-t^2)) is (2e^{2t}(1-t^2)+2e^{2t}t)/((1-t^2)^2)

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\frac{d}{d t} (\frac{e ^{2 t}}{1 - t ^{2}})

\frac{2 e ^{2 t} ( 1 - t ^{2} ) + 2 e ^{2 t} t}{( 1 - t ^{2} ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{e ^{2 t}}{1 - t ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( e ^{2 t} ) ( 1 - t ^{2} ) - \frac{d}{d t} ( 1 - t ^{2} ) e ^{2 t}}{( 1 - t ^{2} ) ^{2}}

\frac{d}{d t} (e^{2 t}) = e^{2 t} \cdot 2

\frac{d}{d t} (1 - t^{2}) = - 2 t

= \frac{e ^{2 t} \cdot 2 ( 1 - t ^{2} ) - ( - 2 t ) e ^{2 t}}{( 1 - t ^{2} ) ^{2}}

Simplify

= \frac{2 e ^{2 t} ( 1 - t ^{2} ) + 2 e ^{2 t} t}{( 1 - t ^{2} ) ^{2}}

\frac{d}{d x} (\frac{x}{x ^{- 1} + 3})

\frac{d}{d x} (cos (\frac{3}{2} x))

n = 1 \sum \infty \frac{1 6 ^{\frac{n}{2}}}{2 ^{2 n}}

\int \frac{1}{e ^{- y}} d y

d y = 2 x (y^{2} + 9) d x

What is the d/(dt)((e^{2t})/(1-t^2)) ?
The d/(dt)((e^{2t})/(1-t^2)) is (2e^{2t}(1-t^2)+2e^{2t}t)/((1-t^2)^2)
What is the first d/(dt)((e^{2t})/(1-t^2)) ?
The first d/(dt)((e^{2t})/(1-t^2)) is (2e^{2t}(1-t^2)+2e^{2t}t)/((1-t^2)^2)