What is the first (sqrt(x^2))^' ?

The first (sqrt(x^2))^' is x/(|x|)

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(sqrt(x^2))^'

(x^{2})^{^{'}}

\frac{x}{∣ x ∣}

Solution steps

(x^{2})^{'}

Apply radical rule:

a^{2} = ∣ a ∣

= (∣ x ∣)^{^{'}}

Apply the common derivative:

(∣ x ∣)^{'} = \frac{x}{∣ x ∣}

= \frac{x}{∣ x ∣}

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\frac{d}{d x} ((\frac{x ^{2} + 1}{x ^{2} - 1})^{7})