What is the derivative of y=(sqrt(x))/(2+x) ?

The derivative of y=(sqrt(x))/(2+x) is (2-x)/(2sqrt(x)(2+x)^2)

What is the first derivative of y=(sqrt(x))/(2+x) ?

The first derivative of y=(sqrt(x))/(2+x) is (2-x)/(2sqrt(x)(2+x)^2)

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derivative of

y = \frac{x}{2 + x}

\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}}

x \to - 2 - lim (- x - 2 + 4)

t \to 2 lim ([e^{- 3 t} i])

\int_{- 5}^{- 7} (- 5)^{- 3} d x

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

y = csc^{2} (x) - 2

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