What is the derivative of g(x)=(sqrt(x))/(4+x) ?

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

What is the first derivative of g(x)=(sqrt(x))/(4+x) ?

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

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derivative of

g (x) = \frac{x}{4 + x}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (7 e^{7 x})

\int 16 x d x

4 e^{t}

\int 2 π d x

n = 0 \sum \infty \frac{n}{n ^{3} + 1}

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