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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d t}{d t} = 1

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

Simplify

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

Popular Examples

sum from n=1 to infinity of 1/(2-e^n)

n = 1 \sum \infty \frac{1}{2 - e ^{n}}

y^{^{'}} = (y - 1)^{2} x^{3}

integral of 2/(e^x)

\int \frac{2}{e ^{x}} d x

integral from 0 to 3 of sqrt(1+x^4+2x^2)

\int_{0}^{3} 1 + x^{4} + 2 x^{2} d x

(x + 4)^{^{'}}

Frequently Asked Questions (FAQ)

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