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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

f (x) = \frac{2}{x}, at x = - 4

\int \frac{x ^{3}}{x ^{4} - 5} d x

\int \frac{x ^{2} - 18 x + 32}{x ( x - 4 ) ^{2}} d x

f (x) = x^{\frac{2}{5}}

2 sin (3 t) + 5 cos (3 t)