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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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