What is the derivative of sqrt(|x^2-6x+5|) ?

The derivative of sqrt(|x^2-6x+5|) is ((x^2-6x+5)(x-3))/(|x^2-6x+5|sqrt(|x^2-6x+5|))

What is the first derivative of sqrt(|x^2-6x+5|) ?

The first derivative of sqrt(|x^2-6x+5|) is ((x^2-6x+5)(x-3))/(|x^2-6x+5|sqrt(|x^2-6x+5|))

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\frac{d}{d x} (∣ x^{2} - 6 x + 5 ∣)

\frac{( x ^{2} - 6 x + 5 ) ( x - 3 )}{∣ x ^{2} - 6 x + 5 ∣ ∣ x ^{2} - 6 x + 5 ∣}

Solution steps

\frac{d}{d x} (∣ x^{2} - 6 x + 5 ∣)

Apply the chain rule:

\frac{1}{2 ∣ x ^{2} - 6 x + 5 ∣} \frac{d}{d x} (x^{2} - 6 x + 5)

= \frac{1}{2 ∣ x ^{2} - 6 x + 5 ∣} \frac{d}{d x} (x^{2} - 6 x + 5)

\frac{d}{d x} (x^{2} - 6 x + 5) = \frac{( x ^{2} - 6 x + 5 ) ( 2 x - 6 )}{∣ x ^{2} - 6 x + 5 ∣}

= \frac{1}{2 ∣ x ^{2} - 6 x + 5 ∣} \cdot \frac{( x ^{2} - 6 x + 5 ) ( 2 x - 6 )}{∣ x ^{2} - 6 x + 5 ∣}

Simplify

\frac{1}{2 ∣ x ^{2} - 6 x + 5 ∣} \cdot \frac{( x ^{2} - 6 x + 5 ) ( 2 x - 6 )}{∣ x ^{2} - 6 x + 5 ∣} : \frac{( x ^{2} - 6 x + 5 ) ( x - 3 )}{∣ x ^{2} - 6 x + 5 ∣ ∣ x ^{2} - 6 x + 5 ∣}

= \frac{( x ^{2} - 6 x + 5 ) ( x - 3 )}{∣ x ^{2} - 6 x + 5 ∣ ∣ x ^{2} - 6 x + 5 ∣}

\int_{0}^{1} \frac{1}{x ^{5}} d x

5 t \frac{d y}{d t} + y = t^{4}

h \to 0 lim (\frac{ln ( e + h ) - 1}{h})

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

\int_{1}^{e} \frac{- 2 ln ( x )}{x ^{2}} d x

What is the derivative of sqrt(|x^2-6x+5|) ?
The derivative of sqrt(|x^2-6x+5|) is ((x^2-6x+5)(x-3))/(|x^2-6x+5|sqrt(|x^2-6x+5|))
What is the first derivative of sqrt(|x^2-6x+5|) ?
The first derivative of sqrt(|x^2-6x+5|) is ((x^2-6x+5)(x-3))/(|x^2-6x+5|sqrt(|x^2-6x+5|))