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

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

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

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

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

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

\frac{d x}{d x} = 1

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

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

1 \cdot (x + 5) - 1 \cdot x = 5

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

\frac{( 1 - x ^{2} ) d y}{d x} = x e^{y}

(2 x - 9)^{4} (x^{2} + x + 1)^{5}

\frac{\partial}{\partial x} (3 y^{2} + x^{2})

\int x (2 x + 1)^{7} d x

\frac{d y}{d x} = x (4 - y)

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