What is the derivative of e^{1/t} ?

The derivative of e^{1/t} is -(e^{1/t})/(t^2)

What is the first derivative of e^{1/t} ?

The first derivative of e^{1/t} is -(e^{1/t})/(t^2)

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derivative of

e^{\frac{1}{t}}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x}{x + 6} d x

\frac{d}{d x} (e^{x} + 2^{(- x)} + 2 cos (x) - 6)

\frac{d y}{d x} + 8 y = e^{x} y^{- 6}

\frac{2 x d y}{d x} + y = 6 x

\frac{d}{d x} (4 x^{3} - 16 x + 5)

What is the derivative of e^{1/t} ?
The derivative of e^{1/t} is -(e^{1/t})/(t^2)
What is the first derivative of e^{1/t} ?
The first derivative of e^{1/t} is -(e^{1/t})/(t^2)