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Popular >

derivative of (1-2x/(1+2x))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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