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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(3/(x^2+z^2))

\frac{\partial}{\partial x} (\frac{3}{x ^{2} + z ^{2}})

(\partial)/(\partial x)(x^3y-y^3)

\frac{\partial}{\partial x} (x^{3} y - y^{3})

derivative of d(x)(55)/(0.01x^2+1)derivative of

d (x) \frac{55}{0.01 x ^{2} + 1}

integral from 1 to 2 of 1/(x^6)

\int_{1}^{2} \frac{1}{x ^{6}} d x

integral of (2x+1)/(x^2)

\int \frac{2 x + 1}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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