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Popular >

derivative of (5x-2/(2x+7))

Solution

\frac{d}{d x} (\frac{5 x - 2}{2 x + 7})

Solution

\frac{39}{( 2 x + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x - 2}{2 x + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x - 2 ) ( 2 x + 7 ) - \frac{d}{d x} ( 2 x + 7 ) ( 5 x - 2 )}{( 2 x + 7 ) ^{2}}

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

\frac{d}{d x} (2 x + 7) = 2

= \frac{5 ( 2 x + 7 ) - 2 ( 5 x - 2 )}{( 2 x + 7 ) ^{2}}

Expand

5 (2 x + 7) - 2 (5 x - 2) : 39

= \frac{39}{( 2 x + 7 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of (5x-2/(2x+7)) ?
The derivative of (5x-2/(2x+7)) is (39)/((2x+7)^2)
What is the first derivative of (5x-2/(2x+7)) ?
The first derivative of (5x-2/(2x+7)) is (39)/((2x+7)^2)