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Popular >

derivative of (8x-1/(3x+8))

Solution

\frac{d}{d x} (\frac{8 x - 1}{3 x + 8})

Solution

\frac{67}{( 3 x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 x - 1}{3 x + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 x - 1 ) ( 3 x + 8 ) - \frac{d}{d x} ( 3 x + 8 ) ( 8 x - 1 )}{( 3 x + 8 ) ^{2}}

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

\frac{d}{d x} (3 x + 8) = 3

= \frac{8 ( 3 x + 8 ) - 3 ( 8 x - 1 )}{( 3 x + 8 ) ^{2}}

Expand

8 (3 x + 8) - 3 (8 x - 1) : 67

= \frac{67}{( 3 x + 8 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of (8x-1/(3x+8)) ?
The derivative of (8x-1/(3x+8)) is (67)/((3x+8)^2)
What is the first derivative of (8x-1/(3x+8)) ?
The first derivative of (8x-1/(3x+8)) is (67)/((3x+8)^2)