What is the derivative of e^{-5/(t^7)} ?

The derivative of e^{-5/(t^7)} is (35e^{-5/(t^7)})/(t^8)

What is the first derivative of e^{-5/(t^7)} ?

The first derivative of e^{-5/(t^7)} is (35e^{-5/(t^7)})/(t^8)

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derivative of

e^{- \frac{5}{t ^{7}}}

\frac{35 e ^{- \frac{5}{t ^{7}}}}{t ^{8}}

Solution steps

\frac{d}{d t} (e^{- \frac{5}{t ^{7}}})

Apply the chain rule:

e^{- \frac{5}{t ^{7}}} \frac{d}{d t} (- \frac{5}{t ^{7}})

= e^{- \frac{5}{t ^{7}}} \frac{d}{d t} (- \frac{5}{t ^{7}})

\frac{d}{d t} (- \frac{5}{t ^{7}}) = \frac{35}{t ^{8}}

= e^{- \frac{5}{t ^{7}}} \frac{35}{t ^{8}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{35 e ^{- \frac{5}{t ^{7}}}}{t ^{8}}

What is the derivative of e^{-5/(t^7)} ?
The derivative of e^{-5/(t^7)} is (35e^{-5/(t^7)})/(t^8)
What is the first derivative of e^{-5/(t^7)} ?
The first derivative of e^{-5/(t^7)} is (35e^{-5/(t^7)})/(t^8)