What is the derivative of (2-3x/(7-x)) ?

The derivative of (2-3x/(7-x)) is -(19)/((7-x)^2)

What is the first derivative of (2-3x/(7-x)) ?

The first derivative of (2-3x/(7-x)) is -(19)/((7-x)^2)

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\frac{d}{d x} (\frac{2 - 3 x}{7 - x})

- \frac{19}{( 7 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 - 3 x}{7 - x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 - 3 x ) ( 7 - x ) - \frac{d}{d x} ( 7 - x ) ( 2 - 3 x )}{( 7 - x ) ^{2}}

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

\frac{d}{d x} (7 - x) = - 1

= \frac{( - 3 ) ( 7 - x ) - ( - 1 ) ( 2 - 3 x )}{( 7 - x ) ^{2}}

Simplify

\frac{( - 3 ) ( 7 - x ) - ( - 1 ) ( 2 - 3 x )}{( 7 - x ) ^{2}} : - \frac{19}{( 7 - x ) ^{2}}

= - \frac{19}{( 7 - x ) ^{2}}

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What is the derivative of (2-3x/(7-x)) ?
The derivative of (2-3x/(7-x)) is -(19)/((7-x)^2)
What is the first derivative of (2-3x/(7-x)) ?
The first derivative of (2-3x/(7-x)) is -(19)/((7-x)^2)