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Popular >

derivative of (5x+4/(5x-4))

Solution

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

Solution

- \frac{40}{( 5 x - 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (5 x + 4) = 5

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

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

Simplify

\frac{5 ( 5 x - 4 ) - 5 ( 5 x + 4 )}{( 5 x - 4 ) ^{2}} : - \frac{40}{( 5 x - 4 ) ^{2}}

= - \frac{40}{( 5 x - 4 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (5x+4/(5x-4)) ?
The derivative of (5x+4/(5x-4)) is -(40)/((5x-4)^2)
What is the first derivative of (5x+4/(5x-4)) ?
The first derivative of (5x+4/(5x-4)) is -(40)/((5x-4)^2)