en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=(x^2)/(x+4)

Solution

derivative of

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

Solution

\frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x + 4})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} ) ( x + 4 ) - \frac{d}{d x} ( x + 4 ) x ^{2}}{( x + 4 ) ^{2}}

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

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

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

Simplify

\frac{2 x ( x + 4 ) - 1 \cdot x ^{2}}{( x + 4 ) ^{2}} : \frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

= \frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

Graph

Popular Examples

sum from n=5 to infinity of 4/(n^2-1)

n = 5 \sum \infty \frac{4}{n ^{2} - 1}

integral of (196)/(x^3-14x^2)

\int \frac{196}{x ^{3} - 14 x ^{2}} d x

integral of 1/(xsqrt(324x^2-324))

\int \frac{1}{x 324 x ^{2} - 324} d x

integral of (9-162x)/(sqrt(16-81x^2))

\int \frac{9 - 162 x}{16 - 81 x ^{2}} d x

integral from 0 to 1 of xcos(5pix)

\int_{0}^{1} x cos (5 π x) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2)/(x+4) ?
The derivative of f(x)=(x^2)/(x+4) is (x^2+8x)/((x+4)^2)
What is the first derivative of f(x)=(x^2)/(x+4) ?
The first derivative of f(x)=(x^2)/(x+4) is (x^2+8x)/((x+4)^2)