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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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