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Popular >

derivative of y=(4x-1)/(2x+5)

Solution

derivative of

y = \frac{4 x - 1}{2 x + 5}

Solution

\frac{22}{( 2 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x - 1}{2 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 - 1 ) ( 2 x + 5 ) - \frac{d}{d x} ( 2 x + 5 ) ( 4 x - 1 )}{( 2 x + 5 ) ^{2}}

\frac{d}{d x} (4 x - 1) = 4

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

= \frac{4 ( 2 x + 5 ) - 2 ( 4 x - 1 )}{( 2 x + 5 ) ^{2}}

Expand

4 (2 x + 5) - 2 (4 x - 1) : 22

= \frac{22}{( 2 x + 5 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of y=(4x-1)/(2x+5) ?
The derivative of y=(4x-1)/(2x+5) is (22)/((2x+5)^2)
What is the first derivative of y=(4x-1)/(2x+5) ?
The first derivative of y=(4x-1)/(2x+5) is (22)/((2x+5)^2)