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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

(dx)/(dy)=(4x+2y+1)

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

derivative of y=(8x^2-16x+16)e^x derivative of

y = (8 x^{2} - 16 x + 16) e^{x}

derivative of (4x/(x+1))

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

(\partial)/(\partial y)(e^{y/x})

\frac{\partial}{\partial y} (e^{\frac{y}{x}})

integral of xsqrt((8-5x^2)^3)

\int x (8 - 5 x^{2})^{3} d x

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)