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Popular Calculus >

derivative of (x^2/(x+10))

Solution

\frac{d}{d x} (\frac{x ^{2}}{x + 10})

Solution

\frac{x ^{2} + 20 x}{( x + 10 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x + 10})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x + 10 ) - \frac{d}{d x} ( x + 10 ) x ^{2}}{( x + 10 ) ^{2}}

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

\frac{d}{d x} (x + 10) = 1

= \frac{2 x ( x + 10 ) - 1 \cdot x ^{2}}{( x + 10 ) ^{2}}

Simplify

\frac{2 x ( x + 10 ) - 1 \cdot x ^{2}}{( x + 10 ) ^{2}} : \frac{x ^{2} + 20 x}{( x + 10 ) ^{2}}

= \frac{x ^{2} + 20 x}{( x + 10 ) ^{2}}

Graph

Popular Examples

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

n = 1 \sum \infty \frac{2}{n ^{2}}

integral of (x^2+5x-8)/(sqrt(x))

\int \frac{x ^{2} + 5 x - 8}{x} d x

limit as x approaches infinity of 2x+8

x \to \infty lim (2 x + 8)

derivative of (2x/(sqrt(1+4x^2)))

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

limit as x approaches 2 of a^2x+2a

x \to 2 lim (a^{2} x + 2 a)

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/(x+10)) ?
The derivative of (x^2/(x+10)) is (x^2+20x)/((x+10)^2)
What is the first derivative of (x^2/(x+10)) ?
The first derivative of (x^2/(x+10)) is (x^2+20x)/((x+10)^2)