derivative of -3cos^2(x) — step-by-step solution

Let's differentiate:

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

We differentiate using:

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

(where f =

\cos (x)

)

ⓘ A constant factor stays in front of the derivative, (k*u)' = k*u':

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

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

■The derivative of x^n is n*x^(n-1):

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

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

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

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

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

- \sin (x)

ⅰ

3 \cdot 2

6

-6 \cdot (- \sin (x)) \cdot \cos (x)

ⓘ Two minus signs cancel out:

-6 \cdot (- \sin (x))

6 \cdot \sin (x)

6 \cdot \sin (x) \cdot \cos (x)

▶Derivative:

6 \cdot \cos (x) \cdot \sin (x)