What is the derivative of (sqrt(x)/(3+x)) ?

The derivative of (sqrt(x)/(3+x)) is (3-x)/(2sqrt(x)(3+x)^2)

What is the first derivative of (sqrt(x)/(3+x)) ?

The first derivative of (sqrt(x)/(3+x)) is (3-x)/(2sqrt(x)(3+x)^2)

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\frac{d}{d x} (\frac{x}{3 + x})

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

Solution steps

\frac{d}{d x} (\frac{x}{3 + x})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (3 + x) = 1

= \frac{\frac{1}{2 x} ( 3 + x ) - 1 \cdot x}{( 3 + x ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( 3 + x ) - 1 \cdot x}{( 3 + x ) ^{2}} : \frac{3 - x}{2 x ( 3 + x ) ^{2}}

= \frac{3 - x}{2 x ( 3 + x ) ^{2}}

\frac{\partial}{\partial t} (cos (t))

x \to 0 lim (4 sin (x) ln (x))

(x^{2} + 1) y^{^{'}} = - 3 x (y - 1)

- \frac{1}{2 x ^{4}}

What is the derivative of (sqrt(x)/(3+x)) ?
The derivative of (sqrt(x)/(3+x)) is (3-x)/(2sqrt(x)(3+x)^2)
What is the first derivative of (sqrt(x)/(3+x)) ?
The first derivative of (sqrt(x)/(3+x)) is (3-x)/(2sqrt(x)(3+x)^2)