What is the derivative of 5/(x^7) ?

The derivative of 5/(x^7) is -(35)/(x^8)

What is the first derivative of 5/(x^7) ?

The first derivative of 5/(x^7) is -(35)/(x^8)

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\frac{d}{d x} (\frac{5}{x ^{7}})

- \frac{35}{x ^{8}}

Solution steps

\frac{d}{d x} (\frac{5}{x ^{7}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (\frac{1}{x ^{7}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 5 (- 7 x^{- 7 - 1})

Simplify

5 (- 7 x^{- 7 - 1}) : - \frac{35}{x ^{8}}

= - \frac{35}{x ^{8}}

- 3 e^{4 t}

\int_{1}^{3} \frac{e ^{x}}{e ^{x} - 1} d x

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\int 7 x e^{3 x} d x

What is the derivative of 5/(x^7) ?
The derivative of 5/(x^7) is -(35)/(x^8)
What is the first derivative of 5/(x^7) ?
The first derivative of 5/(x^7) is -(35)/(x^8)