What is the derivative of-(3x/(8-5x)) ?

The derivative of-(3x/(8-5x)) is -(24)/((8-5x)^2)

What is the first derivative of-(3x/(8-5x)) ?

The first derivative of-(3x/(8-5x)) is -(24)/((8-5x)^2)

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\frac{d}{d x} (- \frac{3 x}{8 - 5 x})

- \frac{24}{( 8 - 5 x ) ^{2}}

Solution steps

\frac{d}{d x} (- \frac{3 x}{8 - 5 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 3 \frac{d}{d x} (\frac{x}{8 - 5 x})

Apply the Quotient Rule:

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

= - 3 \cdot \frac{\frac{d x}{d x} ( 8 - 5 x ) - \frac{d}{d x} ( 8 - 5 x ) x}{( 8 - 5 x ) ^{2}}

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

\frac{d}{d x} (8 - 5 x) = - 5

= - 3 \cdot \frac{1 \cdot ( 8 - 5 x ) - ( - 5 ) x}{( 8 - 5 x ) ^{2}}

Simplify

- 3 \cdot \frac{1 \cdot ( 8 - 5 x ) - ( - 5 ) x}{( 8 - 5 x ) ^{2}} : - \frac{24}{( 8 - 5 x ) ^{2}}

= - \frac{24}{( 8 - 5 x ) ^{2}}

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What is the derivative of-(3x/(8-5x)) ?
The derivative of-(3x/(8-5x)) is -(24)/((8-5x)^2)
What is the first derivative of-(3x/(8-5x)) ?
The first derivative of-(3x/(8-5x)) is -(24)/((8-5x)^2)