What is the derivative of (x^2+2x/(4x)) ?

The derivative of (x^2+2x/(4x)) is 1/4

What is the first derivative of (x^2+2x/(4x)) ?

The first derivative of (x^2+2x/(4x)) is 1/4

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

\frac{1}{4}

Solution steps

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

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{x ^{2} + 2 x}{x})

Apply the Quotient Rule:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( x ^{2} + 2 x ) x - \frac{d x}{d x} ( x ^{2} + 2 x )}{x ^{2}}

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

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

= \frac{1}{4} \cdot \frac{( 2 x + 2 ) x - 1 \cdot ( x ^{2} + 2 x )}{x ^{2}}

Simplify

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

= \frac{1}{4}

\int_{1}^{2} \frac{1}{x ^{8}} d x

n = 1 \sum \infty \frac{2}{( n + 2 ) ^{3}}

\frac{d}{d x} (e^{3 x - 3})

\frac{d}{d x} y = 5 x^{2} cos^{2} (y)

f (x) = 2 x cos (x), at x = \frac{3 π}{2}

What is the derivative of (x^2+2x/(4x)) ?
The derivative of (x^2+2x/(4x)) is 1/4
What is the first derivative of (x^2+2x/(4x)) ?
The first derivative of (x^2+2x/(4x)) is 1/4