What is the derivative of x/(x+6) ?

The derivative of x/(x+6) is 6/((x+6)^2)

What is the first derivative of x/(x+6) ?

The first derivative of x/(x+6) is 6/((x+6)^2)

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derivative of

\frac{x}{x + 6}

\frac{6}{( x + 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 6})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x + 6 ) - \frac{d}{d x} ( x + 6 ) x}{( x + 6 ) ^{2}}

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

\frac{d}{d x} (x + 6) = 1

= \frac{1 \cdot ( x + 6 ) - 1 \cdot x}{( x + 6 ) ^{2}}

1 \cdot (x + 6) - 1 \cdot x = 6

= \frac{6}{( x + 6 ) ^{2}}

\int - \frac{2}{7 - 7 x ^{2}} d x

\frac{d}{d x} (5 x^{3} - 3 x^{5})

t \to - 2 lim ((t + 4)^{2})

x \to - 1 lim (5 x^{2})

x y + y^{^{'}} = 64 x

What is the derivative of x/(x+6) ?
The derivative of x/(x+6) is 6/((x+6)^2)
What is the first derivative of x/(x+6) ?
The first derivative of x/(x+6) is 6/((x+6)^2)