What is the derivative of (sqrt(x)/(x+5)) ?

The derivative of (sqrt(x)/(x+5)) is (-x+5)/(2sqrt(x)(x+5)^2)

What is the first derivative of (sqrt(x)/(x+5)) ?

The first derivative of (sqrt(x)/(x+5)) is (-x+5)/(2sqrt(x)(x+5)^2)

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\frac{d}{d x} (\frac{x}{x + 5})

\frac{- x + 5}{2 x ( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) x}{( x + 5 ) ^{2}}

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

\frac{d}{d x} (x + 5) = 1

= \frac{\frac{1}{2 x} ( x + 5 ) - 1 \cdot x}{( x + 5 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 5 ) - 1 \cdot x}{( x + 5 ) ^{2}} : \frac{- x + 5}{2 x ( x + 5 ) ^{2}}

= \frac{- x + 5}{2 x ( x + 5 ) ^{2}}

\frac{d}{d t} (cos (2 t))

y^{^{''}} - 2 y^{^{'}} + y = x^{2} - 1

y^{^{'}} + 4 y = e^{- t} - 4

\frac{d}{d x} (\frac{3}{2 3 x})

y = (5)^{x}, at x = 6

What is the derivative of (sqrt(x)/(x+5)) ?
The derivative of (sqrt(x)/(x+5)) is (-x+5)/(2sqrt(x)(x+5)^2)
What is the first derivative of (sqrt(x)/(x+5)) ?
The first derivative of (sqrt(x)/(x+5)) is (-x+5)/(2sqrt(x)(x+5)^2)