differentiate cos(2x) — step-by-step solution

Let's differentiate:

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

We differentiate using:

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

(where f =

2 x

)

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

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

- \frac{d}{d x} (2 x) \cdot \sin (2 x)

- \frac{d}{d x} (2 x) \cdot \sin (2 x)

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

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

2

▶Derivative:

- 2 \cdot \sin (2 x)