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Popular >

derivative of (4x-8/(x-5))

Solution

\frac{d}{d x} (\frac{4 x - 8}{x - 5})

Solution

- \frac{12}{( x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x - 8}{x - 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x - 8 ) ( x - 5 ) - \frac{d}{d x} ( x - 5 ) ( 4 x - 8 )}{( x - 5 ) ^{2}}

\frac{d}{d x} (4 x - 8) = 4

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

= \frac{4 ( x - 5 ) - 1 \cdot ( 4 x - 8 )}{( x - 5 ) ^{2}}

Simplify

\frac{4 ( x - 5 ) - 1 \cdot ( 4 x - 8 )}{( x - 5 ) ^{2}} : - \frac{12}{( x - 5 ) ^{2}}

= - \frac{12}{( x - 5 ) ^{2}}

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\int \frac{5 x ^{2} - 5 x + 14}{( x - 2 ) ( x ^{2} + 4 )} d x

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x \to - 3 lim (\frac{x}{x ^{2} - 9})

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\int \frac{1}{2} x e^{2 x} d x

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Frequently Asked Questions (FAQ)

What is the derivative of (4x-8/(x-5)) ?
The derivative of (4x-8/(x-5)) is -(12)/((x-5)^2)
What is the first derivative of (4x-8/(x-5)) ?
The first derivative of (4x-8/(x-5)) is -(12)/((x-5)^2)