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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}}

Popular Examples

slope of 1/(x-4)slope

\frac{1}{x - 4}

limit as x approaches 1+of 2/x-1/(ln(x))

x \to 1 + lim (\frac{2}{x} - \frac{1}{ln ( x )})

(\partial)/(\partial x)(2y*arctan(x/y))

\frac{\partial}{\partial x} (2 y \cdot arctan (\frac{x}{y}))

derivative of 6x+4 derivative of

6 x + 4

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

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

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)