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Popular Calculus >

derivative of (2x-6/(4-x))

Solution

\frac{d}{d x} (\frac{2 x - 6}{4 - x})

Solution

\frac{2}{( 4 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x - 6}{4 - x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x - 6 ) ( 4 - x ) - \frac{d}{d x} ( 4 - x ) ( 2 x - 6 )}{( 4 - x ) ^{2}}

\frac{d}{d x} (2 x - 6) = 2

\frac{d}{d x} (4 - x) = - 1

= \frac{2 ( 4 - x ) - ( - 1 ) ( 2 x - 6 )}{( 4 - x ) ^{2}}

Simplify

\frac{2 ( 4 - x ) - ( - 1 ) ( 2 x - 6 )}{( 4 - x ) ^{2}} : \frac{2}{( 4 - x ) ^{2}}

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

Graph

Popular Examples

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\frac{d}{d x} (\frac{9}{x + 4})

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\frac{d}{d x} (lo g_{6} (cot (8 x)))

limit as x approaches 0 of (tan(3x)-sin(3x))/(x^3)

x \to 0 lim (\frac{tan ( 3 x ) - sin ( 3 x )}{x ^{3}})

derivative of (x^3)/(6x-3)

d er i v a t i v e \frac{x ^{3}}{6 x - 3}

area 3x^2+4,[1,2]

a re a 3 x^{2} + 4, [1, 2]

Frequently Asked Questions (FAQ)

What is the derivative of (2x-6/(4-x)) ?
The derivative of (2x-6/(4-x)) is 2/((4-x)^2)
What is the first derivative of (2x-6/(4-x)) ?
The first derivative of (2x-6/(4-x)) is 2/((4-x)^2)