What is the derivative of 6/(5x^3) ?

The derivative of 6/(5x^3) is -(18)/(5x^4)

What is the first derivative of 6/(5x^3) ?

The first derivative of 6/(5x^3) is -(18)/(5x^4)

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\frac{d}{d x} (\frac{6}{5 x ^{3}})

- \frac{18}{5 x ^{4}}

Solution steps

\frac{d}{d x} (\frac{6}{5 x ^{3}})

Take the constant out:

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

= \frac{6}{5} \frac{d}{d x} (\frac{1}{x ^{3}})

Apply exponent rule:

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

= \frac{6}{5} \frac{d}{d x} (x^{- 3})

Apply the Power Rule:

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

= \frac{6}{5} (- 3 x^{- 3 - 1})

Simplify

\frac{6}{5} (- 3 x^{- 3 - 1}) : - \frac{18}{5 x ^{4}}

= - \frac{18}{5 x ^{4}}

What is the derivative of 6/(5x^3) ?
The derivative of 6/(5x^3) is -(18)/(5x^4)
What is the first derivative of 6/(5x^3) ?
The first derivative of 6/(5x^3) is -(18)/(5x^4)