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Popular >

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

Solution

derivative of

\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

integral of e^{-0.06x}

\int e^{- 0.06 x} d x

(\partial)/(\partial y)(sin(x-y)+(xy))

\frac{\partial}{\partial y} (sin (x - y) + (x y))

(\partial)/(\partial x)(-4x^2y-4x)

\frac{\partial}{\partial x} (- 4 x^{2} y - 4 x)

derivative of (x^2+4x+8/((x+2)^2))

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

derivative of f(x)=-x^{4/3}derivative of

f (x) = - x^{\frac{4}{3}}

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)