What is the derivative of (4x-12/((x-2)^2)) ?

The derivative of (4x-12/((x-2)^2)) is (4(-x+4))/((x-2)^3)

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

The first derivative of (4x-12/((x-2)^2)) is (4(-x+4))/((x-2)^3)

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\frac{d}{d x} (\frac{4 x - 12}{( x - 2 ) ^{2}})

\frac{4 ( - x + 4 )}{( x - 2 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{4 x - 12}{( x - 2 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x - 12 ) ( x - 2 ) ^{2} - \frac{d}{d x} ( ( x - 2 ) ^{2} ) ( 4 x - 12 )}{( ( x - 2 ) ^{2} ) ^{2}}

\frac{d}{d x} (4 x - 12) = 4

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

= \frac{4 ( x - 2 ) ^{2} - 2 ( x - 2 ) ( 4 x - 12 )}{( ( x - 2 ) ^{2} ) ^{2}}

Simplify

\frac{4 ( x - 2 ) ^{2} - 2 ( x - 2 ) ( 4 x - 12 )}{( ( x - 2 ) ^{2} ) ^{2}} : \frac{4 ( - x + 4 )}{( x - 2 ) ^{3}}

= \frac{4 ( - x + 4 )}{( x - 2 ) ^{3}}

\frac{d}{d x} (- 2.67 + 1.29 x + 6.28 x^{2} + 2.4 x^{3})

x \to 3 - lim (3 - x)

\int x^{7} x^{4} + 3 d x

f (x) = \frac{3}{x + 1}, (2, 1)

y^{^{'}} = e^{- 3 x} + 2 x

What is the derivative of (4x-12/((x-2)^2)) ?
The derivative of (4x-12/((x-2)^2)) is (4(-x+4))/((x-2)^3)
What is the first derivative of (4x-12/((x-2)^2)) ?
The first derivative of (4x-12/((x-2)^2)) is (4(-x+4))/((x-2)^3)