What is the derivative of (cos(x)^3) ?

The derivative of (cos(x)^3) is -3cos^2(x)sin(x)

What is the first derivative of (cos(x)^3) ?

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

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\frac{d}{d x} ((cos (x))^{3})

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

Solution steps

\frac{d}{d x} ((cos (x))^{3})

Apply the chain rule:

3 (cos (x))^{2} \frac{d}{d x} (cos (x))

= 3 (cos (x))^{2} \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

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

Simplify

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

x^{^{'}} + \frac{2}{1 + t} x = \frac{e ^{t}}{1 + t}

\int_{- 1}^{1} 3 x^{2} x^{3} + 5 d x

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

x \to 1 + lim (\frac{5}{x ^{3} - 1})

\int \frac{x + 5}{x ^{2} + 10 x} d x

What is the derivative of (cos(x)^3) ?
The derivative of (cos(x)^3) is -3cos^2(x)sin(x)
What is the first derivative of (cos(x)^3) ?
The first derivative of (cos(x)^3) is -3cos^2(x)sin(x)