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

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

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

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

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derivative of

\frac{2 x}{x + 2}

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

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

Simplify

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

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

\int \frac{x ^{2} + 1}{x ^{2}} d x

x e^{y} d y + \frac{x ^{2} + 1}{y} d x = 0

\frac{d}{d x} (\frac{1 - 2 x}{1 + 2 x})

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

(3 x^{3} + 2 x) (x - 2) (x + 4)

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