What is the derivative of 8/(5x^4) ?

The derivative of 8/(5x^4) is -(32)/(5x^5)

What is the first derivative of 8/(5x^4) ?

The first derivative of 8/(5x^4) is -(32)/(5x^5)

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\frac{d}{d x} (\frac{8}{5 x ^{4}})

- \frac{32}{5 x ^{5}}

Solution steps

\frac{d}{d x} (\frac{8}{5 x ^{4}})

Take the constant out:

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

= \frac{8}{5} \frac{d}{d x} (\frac{1}{x ^{4}})

Apply exponent rule:

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

= \frac{8}{5} \frac{d}{d x} (x^{- 4})

Apply the Power Rule:

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

= \frac{8}{5} (- 4 x^{- 4 - 1})

Simplify

\frac{8}{5} (- 4 x^{- 4 - 1}) : - \frac{32}{5 x ^{5}}

= - \frac{32}{5 x ^{5}}

What is the derivative of 8/(5x^4) ?
The derivative of 8/(5x^4) is -(32)/(5x^5)
What is the first derivative of 8/(5x^4) ?
The first derivative of 8/(5x^4) is -(32)/(5x^5)