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Popular Calculus >

derivative of (5x-1)/(x+5)

Solution

derivative of

\frac{5 x - 1}{x + 5}

Solution

\frac{26}{( x + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (5 x - 1) = 5

\frac{d}{d x} (x + 5) = 1

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

Simplify

\frac{5 ( x + 5 ) - 1 \cdot ( 5 x - 1 )}{( x + 5 ) ^{2}} : \frac{26}{( x + 5 ) ^{2}}

= \frac{26}{( x + 5 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (5x-1)/(x+5) ?
The derivative of (5x-1)/(x+5) is (26)/((x+5)^2)
What is the first derivative of (5x-1)/(x+5) ?
The first derivative of (5x-1)/(x+5) is (26)/((x+5)^2)