What is the derivative of (2x/(2x+1)) ?

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

f (x) = ln (1 - 3 x)

\int_{0}^{N} e^{(- s t)} sin (5 t) d t

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

\int \frac{1}{x - 1} d x

x \to 2 lim (2 - x^{2})

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