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

The derivative of (2x)/(2+sqrt(x)) is (4+sqrt(x))/((2+sqrt(x))^2)

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

The first derivative of (2x)/(2+sqrt(x)) is (4+sqrt(x))/((2+sqrt(x))^2)

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derivative of

\frac{2 x}{2 + x}

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

2 \cdot \frac{1 \cdot ( 2 + x ) - \frac{1}{2 x} x}{( 2 + x ) ^{2}} : \frac{4 + x}{( 2 + x ) ^{2}}

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

\int sin^{2} (8 x) d x

\frac{d}{d x} (5 x^{4} - 60 x^{2} + 64)

\int e^{x} x^{- 1} d x

\int_{2}^{\infty} e^{- 8 x} d x

y^{^{'}} = e^{x} y

What is the derivative of (2x)/(2+sqrt(x)) ?
The derivative of (2x)/(2+sqrt(x)) is (4+sqrt(x))/((2+sqrt(x))^2)
What is the first derivative of (2x)/(2+sqrt(x)) ?
The first derivative of (2x)/(2+sqrt(x)) is (4+sqrt(x))/((2+sqrt(x))^2)