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

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

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

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

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derivative of

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

- \frac{6}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= - \frac{6}{x ^{2}}

ln (\frac{9}{x})

e^{x} - 2

\frac{w \cdot v t x ^{2} + x}{x ^{2} + 2 x + 7}

\frac{d}{d r} (3.14 r^{3})

y = 5 x^{2} - 6 x + 12

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