What is the (cos^4(x))^' ?

The (cos^4(x))^' is -4cos^3(x)sin(x)

What is the first (cos^4(x))^' ?

The first (cos^4(x))^' is -4cos^3(x)sin(x)

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(cos^{4} (x))^{^{'}}

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

Solution steps

(cos^{4} (x))^{'}

Apply the chain rule:

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

= 4 (cos (x))^{3} (cos (x))^{'}

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

= 4 (cos (x))^{3} (- sin (x))

Simplify

= - 4 cos^{3} (x) sin (x)

x \to 0 lim (\frac{sin ( - 4 x )}{x})

\int \frac{x ^{6}}{x ^{14} - 9} d x

4 + 3 x

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

x = y^{2} - 2, x = 6 - y^{2}