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Popular >

derivative of (8x-1/(6x+7))

Solution

\frac{d}{d x} (\frac{8 x - 1}{6 x + 7})

Solution

\frac{62}{( 6 x + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 x - 1}{6 x + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 x - 1 ) ( 6 x + 7 ) - \frac{d}{d x} ( 6 x + 7 ) ( 8 x - 1 )}{( 6 x + 7 ) ^{2}}

\frac{d}{d x} (8 x - 1) = 8

\frac{d}{d x} (6 x + 7) = 6

= \frac{8 ( 6 x + 7 ) - 6 ( 8 x - 1 )}{( 6 x + 7 ) ^{2}}

Expand

8 (6 x + 7) - 6 (8 x - 1) : 62

= \frac{62}{( 6 x + 7 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of (8x-1/(6x+7)) ?
The derivative of (8x-1/(6x+7)) is (62)/((6x+7)^2)
What is the first derivative of (8x-1/(6x+7)) ?
The first derivative of (8x-1/(6x+7)) is (62)/((6x+7)^2)