derivative of (cos(x)^3) — step-by-step solution

Let's differentiate:

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

Apply the differentiation rule:

\frac{d}{d x} (f^{n}) = n \cdot \frac{d}{d x} (f) \cdot f^{n - 1}

with f =

\cos (x)

ⓘ The derivative of x^n is n*x^(n-1):

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

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

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

ⓘ The derivative of cos(x) is -sin(x):

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

- \sin (x)

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

ⓘ The minus sign is placed in front of the product:

3 \cdot (- \sin (x))

-3 \cdot \sin (x)

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

▶Derivative:

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