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Popular Calculus >

derivative of (3+8x)/(9-2x)

Solution

derivative of

\frac{3 + 8 x}{9 - 2 x}

Solution

\frac{78}{( 9 - 2 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 + 8 x}{9 - 2 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 + 8 x ) ( 9 - 2 x ) - \frac{d}{d x} ( 9 - 2 x ) ( 3 + 8 x )}{( 9 - 2 x ) ^{2}}

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

\frac{d}{d x} (9 - 2 x) = - 2

= \frac{8 ( 9 - 2 x ) - ( - 2 ) ( 3 + 8 x )}{( 9 - 2 x ) ^{2}}

Simplify

\frac{8 ( 9 - 2 x ) - ( - 2 ) ( 3 + 8 x )}{( 9 - 2 x ) ^{2}} : \frac{78}{( 9 - 2 x ) ^{2}}

= \frac{78}{( 9 - 2 x ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (3+8x)/(9-2x) ?
The derivative of (3+8x)/(9-2x) is (78)/((9-2x)^2)
What is the first derivative of (3+8x)/(9-2x) ?
The first derivative of (3+8x)/(9-2x) is (78)/((9-2x)^2)