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Popular >

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

Solution

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

Solution

\frac{1}{2}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{1}{2}

Popular Examples

integral of (x^4+x^3+x^2+1)/(x^2+x-2)

\int \frac{x ^{4} + x ^{3} + x ^{2} + 1}{x ^{2} + x - 2} d x

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\frac{d}{d x} (\frac{4 x}{5 x ^{2} + 3})

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\int \frac{8}{36 x ^{2} + 4} d x

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

(\partial)/(\partial v)(3usin(v))

\frac{\partial}{\partial v} (3 u sin (v))

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/(2x)) ?
The derivative of (x^2/(2x)) is 1/2
What is the first derivative of (x^2/(2x)) ?
The first derivative of (x^2/(2x)) is 1/2