What is the derivative of 8/(x^7) ?

The derivative of 8/(x^7) is -(56)/(x^8)

What is the first derivative of 8/(x^7) ?

The first derivative of 8/(x^7) is -(56)/(x^8)

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\frac{d}{d x} (\frac{8}{x ^{7}})

- \frac{56}{x ^{8}}

Solution steps

\frac{d}{d x} (\frac{8}{x ^{7}})

Take the constant out:

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

= 8 \frac{d}{d x} (\frac{1}{x ^{7}})

Apply exponent rule:

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

= 8 \frac{d}{d x} (x^{- 7})

Apply the Power Rule:

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

= 8 (- 7 x^{- 7 - 1})

Simplify

8 (- 7 x^{- 7 - 1}) : - \frac{56}{x ^{8}}

= - \frac{56}{x ^{8}}

What is the derivative of 8/(x^7) ?
The derivative of 8/(x^7) is -(56)/(x^8)
What is the first derivative of 8/(x^7) ?
The first derivative of 8/(x^7) is -(56)/(x^8)