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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

\frac{d}{d x} (10 - x)

x \to 0 lim (\frac{2 - 2 cos ( x )}{e ^{x} - x - 1})

\int \frac{( ln ( x ) )}{x ^{2}} d x

\frac{\partial}{\partial x} (x^{8} y^{6} - x^{7} y^{5})

x \to \infty lim (7^{- x})

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