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)

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

- \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}}

\frac{\partial}{\partial x} (8 x^{5} y^{6} + 6 x^{4} y^{8})

6 x^{- 4}

\frac{\partial}{\partial x} (5 y^{\frac{1}{4}} x^{\frac{1}{2}})

\int x^{3} 4 + x^{4} d x

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)