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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}}

Graph

Popular Examples

area f(x)=4-x,-2,6 area

f (x) = 4 - x, - 2, 6

integral from 5 to 9 of 2/(x^3)

\int_{5}^{9} \frac{2}{x ^{3}} d x

integral of e^{3x}sqrt(1+2e^{3x)}

\int e^{3 x} 1 + 2 e^{3 x} d x

(\partial)/(\partial x)(1-2x^2-2y)

\frac{\partial}{\partial x} (1 - 2 x^{2} - 2 y)

(1-t^2)y^{''}-2ty^'+2y=0

(1 - t^{2}) y^{^{''}} - 2 t y^{^{'}} + 2 y = 0

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)