What is the (ln^3(x))^' ?

The (ln^3(x))^' is (3ln^2(x))/x

What is the first (ln^3(x))^' ?

The first (ln^3(x))^' is (3ln^2(x))/x

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(ln^{3} (x))^{^{'}}

\frac{3 ln ^{2} ( x )}{x}

Solution steps

(ln^{3} (x))^{'}

Apply the chain rule:

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

= 3 (ln (x))^{2} (ln (x))^{'}

(ln (x))^{'} = \frac{1}{x}

= 3 (ln (x))^{2} \frac{1}{x}

Simplify

3 ln^{2} (x) \frac{1}{x} : \frac{3 ln ^{2} ( x )}{x}

= \frac{3 ln ^{2} ( x )}{x}

\int (sin (x))^{5} (cos (x))^{3} d x

\frac{d ^{2}}{d x ^{2}} (1 + \frac{1}{x ^{4}})

\frac{3}{x}

(\frac{d x}{d y}) + 3 x y^{3} = 0

x + 19