What is the derivative of (2x-6)/(x-6) ?

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

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

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

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derivative of

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

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

Solution steps

\frac{d}{d x} (\frac{2 x - 6}{x - 6})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{\frac{1}{x}}{ln ( x )} d x

\frac{e ^{- x}}{1 + e ^{- x}}

\frac{d}{d x} (2 (1 - sin (x)))

\int 8 x e^{4 x^{2}} d x

sin (x), \frac{π}{5}

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