What is the derivative of y=(x/(1+x))^5 ?

The derivative of y=(x/(1+x))^5 is (5x^4)/((1+x)^6)

What is the first derivative of y=(x/(1+x))^5 ?

The first derivative of y=(x/(1+x))^5 is (5x^4)/((1+x)^6)

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derivative of

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

\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}}

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