en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

derivative of

y = (\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}}

Popular Examples

derivative of 2x*e^{x^2}

\frac{d}{d x} (2 x \cdot e^{x^{2}})

limit as x approaches 25 of sqrt(x)-5

x \to 25 lim (x - 5)

derivative of x/(3+e^x)

\frac{d}{d x} (\frac{x}{3 + e ^{x}})

integral of 2+x-x^2

\int 2 + x - x^{2} d x

integral of ((6x+7))/((x+2)^2)

\int \frac{( 6 x + 7 )}{( x + 2 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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)