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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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t \to 0 lim (\frac{sin ( k t )}{t})

derivative of f(x)= x/a derivative of

f (x) = \frac{x}{a}

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f (x) = x^{2} (4 - x)^{2}, at x = 1

integral from 0 to 1 of 1/(1-x^2)

\int_{0}^{1} \frac{1}{1 - x ^{2}} d x

limit as x approaches 0 of 3/(e^x+1)

x \to 0 lim (\frac{3}{e ^{x} + 1})

Frequently Asked Questions (FAQ)

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