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Popular >

derivative of (x/(1+x)^5)

Solution

\frac{d}{d x} ((\frac{x}{1 + x})^{5})

Solution

\frac{5 x ^{4}}{( 1 + x ) ^{6}}

Solution steps

\frac{d}{d x} ((\frac{x}{1 + x})^{5})

Apply the chain rule:

5 (\frac{x}{1 + x})^{4} \frac{d}{d x} (\frac{x}{1 + x})

= 5 (\frac{x}{1 + x})^{4} \frac{d}{d x} (\frac{x}{1 + x})

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

= 5 (\frac{x}{1 + x})^{4} \frac{1}{( 1 + x ) ^{2}}

Simplify

5 (\frac{x}{1 + x})^{4} \frac{1}{( 1 + x ) ^{2}} : \frac{5 x ^{4}}{( 1 + x ) ^{6}}

= \frac{5 x ^{4}}{( 1 + x ) ^{6}}

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Frequently Asked Questions (FAQ)

What is the derivative of (x/(1+x)^5) ?
The derivative of (x/(1+x)^5) is (5x^4)/((1+x)^6)
What is the first derivative of (x/(1+x)^5) ?
The first derivative of (x/(1+x)^5) is (5x^4)/((1+x)^6)