What is the derivative of (x/(x+1)^{2016}) ?

The derivative of (x/(x+1)^{2016}) is (2016x^{2015})/((x+1)^{2017)}

What is the first derivative of (x/(x+1)^{2016}) ?

The first derivative of (x/(x+1)^{2016}) is (2016x^{2015})/((x+1)^{2017)}

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\frac{d}{d x} ((\frac{x}{x + 1})^{2016})

\frac{2016 x ^{2015}}{( x + 1 ) ^{2017}}

Solution steps

\frac{d}{d x} ((\frac{x}{x + 1})^{2016})

Apply the chain rule:

2016 (\frac{x}{x + 1})^{2015} \frac{d}{d x} (\frac{x}{x + 1})

= 2016 (\frac{x}{x + 1})^{2015} \frac{d}{d x} (\frac{x}{x + 1})

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

= 2016 (\frac{x}{x + 1})^{2015} \frac{1}{( x + 1 ) ^{2}}

Simplify

2016 (\frac{x}{x + 1})^{2015} \frac{1}{( x + 1 ) ^{2}} : \frac{2016 x ^{2015}}{( x + 1 ) ^{2017}}

= \frac{2016 x ^{2015}}{( x + 1 ) ^{2017}}

\int \frac{1}{P - Z} + \frac{1}{Z} d Z

n = 1 \sum \infty \frac{3 n}{n !}

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What is the derivative of (x/(x+1)^{2016}) ?
The derivative of (x/(x+1)^{2016}) is (2016x^{2015})/((x+1)^{2017)}
What is the first derivative of (x/(x+1)^{2016}) ?
The first derivative of (x/(x+1)^{2016}) is (2016x^{2015})/((x+1)^{2017)}