What is the derivative of ((1-2x)/(1+x))^3 ?

The derivative of ((1-2x)/(1+x))^3 is -(9(1-2x)^2)/((1+x)^4)

What is the first derivative of ((1-2x)/(1+x))^3 ?

The first derivative of ((1-2x)/(1+x))^3 is -(9(1-2x)^2)/((1+x)^4)

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derivative of

(\frac{1 - 2 x}{1 + x})^{3}

- \frac{9 ( 1 - 2 x ) ^{2}}{( 1 + x ) ^{4}}

Solution steps

\frac{d}{d x} ((\frac{1 - 2 x}{1 + x})^{3})

Apply the chain rule:

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

= 3 (\frac{1 - 2 x}{1 + x})^{2} \frac{d}{d x} (\frac{1 - 2 x}{1 + x})

\frac{d}{d x} (\frac{1 - 2 x}{1 + x}) = - \frac{3}{( 1 + x ) ^{2}}

= 3 (\frac{1 - 2 x}{1 + x})^{2} (- \frac{3}{( 1 + x ) ^{2}})

Simplify

3 (\frac{1 - 2 x}{1 + x})^{2} (- \frac{3}{( 1 + x ) ^{2}}) : - \frac{9 ( 1 - 2 x ) ^{2}}{( 1 + x ) ^{4}}

= - \frac{9 ( 1 - 2 x ) ^{2}}{( 1 + x ) ^{4}}

What is the derivative of ((1-2x)/(1+x))^3 ?
The derivative of ((1-2x)/(1+x))^3 is -(9(1-2x)^2)/((1+x)^4)
What is the first derivative of ((1-2x)/(1+x))^3 ?
The first derivative of ((1-2x)/(1+x))^3 is -(9(1-2x)^2)/((1+x)^4)