What is the derivative of x/(x+13) ?

The derivative of x/(x+13) is (13)/((x+13)^2)

What is the first derivative of x/(x+13) ?

The first derivative of x/(x+13) is (13)/((x+13)^2)

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\frac{d}{d x} (\frac{x}{x + 13})

\frac{13}{( x + 13 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 13})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x + 13 ) - \frac{d}{d x} ( x + 13 ) x}{( x + 13 ) ^{2}}

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

\frac{d}{d x} (x + 13) = 1

= \frac{1 \cdot ( x + 13 ) - 1 \cdot x}{( x + 13 ) ^{2}}

1 \cdot (x + 13) - 1 \cdot x = 13

= \frac{13}{( x + 13 ) ^{2}}

x \frac{d y}{d x} + 5 y = 7 x^{2}

\frac{d}{d x} ((x + 1) e^{- x})

\int \frac{9}{x ^{8}} d x

\int_{0}^{10} x^{2} - 8 x + 7 d x

\frac{\partial}{\partial y} (7 x + 5 y)

What is the derivative of x/(x+13) ?
The derivative of x/(x+13) is (13)/((x+13)^2)
What is the first derivative of x/(x+13) ?
The first derivative of x/(x+13) is (13)/((x+13)^2)