What is the derivative of (x-5/(3x-4)) ?

The derivative of (x-5/(3x-4)) is (11)/((3x-4)^2)

What is the first derivative of (x-5/(3x-4)) ?

The first derivative of (x-5/(3x-4)) is (11)/((3x-4)^2)

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\frac{d}{d x} (\frac{x - 5}{3 x - 4})

\frac{11}{( 3 x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{3 x - 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( 3 x - 4 ) - \frac{d}{d x} ( 3 x - 4 ) ( x - 5 )}{( 3 x - 4 ) ^{2}}

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

\frac{d}{d x} (3 x - 4) = 3

= \frac{1 \cdot ( 3 x - 4 ) - 3 ( x - 5 )}{( 3 x - 4 ) ^{2}}

Simplify

\frac{1 \cdot ( 3 x - 4 ) - 3 ( x - 5 )}{( 3 x - 4 ) ^{2}} : \frac{11}{( 3 x - 4 ) ^{2}}

= \frac{11}{( 3 x - 4 ) ^{2}}

What is the derivative of (x-5/(3x-4)) ?
The derivative of (x-5/(3x-4)) is (11)/((3x-4)^2)
What is the first derivative of (x-5/(3x-4)) ?
The first derivative of (x-5/(3x-4)) is (11)/((3x-4)^2)