What is the derivative of (4x-7/(x-2)) ?

The derivative of (4x-7/(x-2)) is -1/((x-2)^2)

What is the first derivative of (4x-7/(x-2)) ?

The first derivative of (4x-7/(x-2)) is -1/((x-2)^2)

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\frac{d}{d x} (\frac{4 x - 7}{x - 2})

- \frac{1}{( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x - 7}{x - 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x - 7 ) ( x - 2 ) - \frac{d}{d x} ( x - 2 ) ( 4 x - 7 )}{( x - 2 ) ^{2}}

\frac{d}{d x} (4 x - 7) = 4

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

= \frac{4 ( x - 2 ) - 1 \cdot ( 4 x - 7 )}{( x - 2 ) ^{2}}

Simplify

\frac{4 ( x - 2 ) - 1 \cdot ( 4 x - 7 )}{( x - 2 ) ^{2}} : - \frac{1}{( x - 2 ) ^{2}}

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

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

x + \frac{6}{x}

\int - cos (x) d x

x^{4} sin (x) tan (x)

x \to 4 lim (\frac{x + 5 - 3}{x - 4})

What is the derivative of (4x-7/(x-2)) ?
The derivative of (4x-7/(x-2)) is -1/((x-2)^2)
What is the first derivative of (4x-7/(x-2)) ?
The first derivative of (4x-7/(x-2)) is -1/((x-2)^2)