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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

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\frac{s}{s ^{2} + 9}

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\int 3 x^{3} e^{- x^{2}} d x

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y = \frac{1}{7 t + 3}

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\int_{0}^{15} \frac{x}{x + 1} d x

Frequently Asked Questions (FAQ)

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