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

The (sin^3(x))^' is 3sin^2(x)cos(x)

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

The first (sin^3(x))^' is 3sin^2(x)cos(x)

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

3 sin^{2} (x) cos (x)

Solution steps

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

Apply the chain rule:

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

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

(sin (x))^{'} = cos (x)

= 3 (sin (x))^{2} cos (x)

Simplify

= 3 sin^{2} (x) cos (x)

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

x \to - 8 lim (\frac{8 - ∣ x ∣}{8 + x})

\int \frac{14}{x ^{2} - 1} d x

\frac{d}{d x} (ln (x^{2} - 12 x))

\int 4 sin^{5} (x) cos (x) d x