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Popular >

derivative of e^{-5/(t^7)}

Solution

derivative of

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

Solution

\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}}

Popular Examples

derivative of ln(2x-1)derivative of

ln (2 x - 1)

integral of-x^7e^{x^8-7}-2x

\int - x^{7} e^{x^{8} - 7} - 2 x d x

derivative of (cos(x)/(2sin^2(x)))

\frac{d}{d x} (\frac{cos ( x )}{2 sin ^{2} ( x )})

derivative of e^{1/(sqrt(x)})

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

derivative of x^{-2}(4+3x^{-3})

\frac{d}{d x} (x^{- 2} (4 + 3 x^{- 3}))

Frequently Asked Questions (FAQ)

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)