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Popular Calculus >

derivative of (2x/(x^3))

Solution

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

Solution

- \frac{4}{x ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

2 \cdot \frac{1 \cdot x ^{3} - 3 x ^{2} x}{( x ^{3} ) ^{2}} : - \frac{4}{x ^{3}}

= - \frac{4}{x ^{3}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (2x/(x^3)) ?
The derivative of (2x/(x^3)) is -4/(x^3)
What is the first derivative of (2x/(x^3)) ?
The first derivative of (2x/(x^3)) is -4/(x^3)