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Popular Calculus >

derivative of (2x-5/(2x+5))

Solution

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

Solution

\frac{20}{( 2 x + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

2 (2 x + 5) - 2 (2 x - 5) : 20

= \frac{20}{( 2 x + 5 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (2x-5/(2x+5)) ?
The derivative of (2x-5/(2x+5)) is (20)/((2x+5)^2)
What is the first derivative of (2x-5/(2x+5)) ?
The first derivative of (2x-5/(2x+5)) is (20)/((2x+5)^2)