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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

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

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

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

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

Simplify

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

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

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