What is the derivative of (3+2x/(5-8x)) ?

The derivative of (3+2x/(5-8x)) is (34)/((5-8x)^2)

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

The first derivative of (3+2x/(5-8x)) is (34)/((5-8x)^2)

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\frac{d}{d x} (\frac{3 + 2 x}{5 - 8 x})

\frac{34}{( 5 - 8 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 + 2 x}{5 - 8 x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( 5 - 8 x ) - ( - 8 ) ( 3 + 2 x )}{( 5 - 8 x ) ^{2}} : \frac{34}{( 5 - 8 x ) ^{2}}

= \frac{34}{( 5 - 8 x ) ^{2}}

What is the derivative of (3+2x/(5-8x)) ?
The derivative of (3+2x/(5-8x)) is (34)/((5-8x)^2)
What is the first derivative of (3+2x/(5-8x)) ?
The first derivative of (3+2x/(5-8x)) is (34)/((5-8x)^2)