derivative of sin(3x+1) — step-by-step solution

Let's differentiate:

\frac{d}{d x} (\sin (3 x + 1))

We differentiate using:

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

(where f =

3 x + 1

)

ⓘ The derivative of sin(x) is cos(x):

\frac{d}{d x} (\sin (3 x + 1))

\frac{d}{d x} (3 x + 1) \cdot \cos (3 x + 1)

\frac{d}{d x} (3 x + 1) \cdot \cos (3 x + 1)

ⓘ The derivative of a sum is the sum of the derivatives:

\frac{d}{d x} (3 x + 1)

\frac{d}{d x} (3 x) + 0

(\frac{d}{d x} (3 x) + 0) \cdot \cos (3 x + 1)

ⓘ Adding 0 changes nothing:

\frac{d}{d x} (3 x) + 0

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

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

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

3

▶Derivative:

3 \cdot \cos (3 x + 1)