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

The derivative of (x^2-x-2)/(|x-2|) is (x-2)/(|x-2|)

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

The first derivative of (x^2-x-2)/(|x-2|) is (x-2)/(|x-2|)

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derivative of

\frac{x ^{2} - x - 2}{∣ x - 2 ∣}

\frac{x - 2}{∣ x - 2 ∣}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{x - 2}{∣ x - 2 ∣}

\frac{( a + 2 )}{( a + x )}

\frac{d}{d p} (20 p)

m (t) = 20 e^{0.8} t

x + 3 g

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

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