What is the derivative of (2a^3/x) ?

The derivative of (2a^3/x) is -(2a^3)/(x^2)

What is the first derivative of (2a^3/x) ?

The first derivative of (2a^3/x) is -(2a^3)/(x^2)

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\frac{d}{d x} (\frac{2 a ^{3}}{x})

- \frac{2 a ^{3}}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 a ^{3}}{x})

Take the constant out:

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

= 2 a^{3} \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

= 2 a^{3} \frac{d}{d x} (x^{- 1})

Apply the Power Rule:

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

= 2 a^{3} (- 1 \cdot x^{- 1 - 1})

Simplify

2 a^{3} (- 1 \cdot x^{- 1 - 1}) : - \frac{2 a ^{3}}{x ^{2}}

= - \frac{2 a ^{3}}{x ^{2}}

What is the derivative of (2a^3/x) ?
The derivative of (2a^3/x) is -(2a^3)/(x^2)
What is the first derivative of (2a^3/x) ?
The first derivative of (2a^3/x) is -(2a^3)/(x^2)