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Popular >

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

Solution

derivative of

\frac{4 x + 5}{4 x - 5}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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