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

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

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

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

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derivative of

\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 8 t e^{t} d t

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

l a pl a ce t r an s f or m 8 t^{2}

y^{^{'}} + 2 y = 60, y (1) = 80

d er i v a t i v e f (x) = 3 sin (x) + cos (x)

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