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

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

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

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

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derivative of

f (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}}

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

\int x^{3} x^{2} - 9 d x

\frac{d y}{d x} = 2^{x - y}, y (- 3) = - 5

\int \frac{4 x + 8}{( x + 5 ) ^{2}} d x

\frac{1}{4 x ^{\frac{3}{4}}}

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