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

The derivative of (|x-2|)/(x^2) is (-x^2+6x-8)/(x^3|x-2|)

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

The first derivative of (|x-2|)/(x^2) is (-x^2+6x-8)/(x^3|x-2|)

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derivative of

\frac{∣ x - 2 ∣}{x ^{2}}

\frac{- x ^{2} + 6 x - 8}{x ^{3} ∣ x - 2 ∣}

Solution steps

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

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

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

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

Simplify

\frac{\frac{x - 2}{∣ x - 2 ∣} x ^{2} - 2 x ∣ x - 2 ∣}{( x ^{2} ) ^{2}} : \frac{- x ^{2} + 6 x - 8}{x ^{3} ∣ x - 2 ∣}

= \frac{- x ^{2} + 6 x - 8}{x ^{3} ∣ x - 2 ∣}

\frac{d}{d x} (\frac{100}{( 1 + 5 x ) ^{3}})

\int \frac{1 + tan ( x )}{1 - tan ( x )} d x

x \to \infty lim ((1 - \frac{1}{4 x})^{8 x})

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

\int (5 x - 1) (3 x^{2} + 2) d x

What is the derivative of (|x-2|)/(x^2) ?
The derivative of (|x-2|)/(x^2) is (-x^2+6x-8)/(x^3|x-2|)
What is the first derivative of (|x-2|)/(x^2) ?
The first derivative of (|x-2|)/(x^2) is (-x^2+6x-8)/(x^3|x-2|)