differentiate sin(3x) — step-by-step solution

Let's differentiate:

\frac{d}{d x} (\sin (3 x))

Apply the differentiation rule:

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

with f =

3 x

ⓘ The derivative of

\sin (x)

\cos (x)

\frac{d}{d x} (\sin (3 x))

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

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

ⓘ A constant factor stays in front of the derivative: that of

k u

k \cdot u'

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

3

▶Derivative:

3 \cdot \cos (3 x)