derivative of sin(x^2+3x+1) — step-by-step solution

Let's differentiate:

\frac{d}{d x} (\sin (x^{2} + 3 x + 1))

Apply the differentiation rule:

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

with f =

x^{2} + 3 x + 1

\frac{d}{d x} (x^{2} + 3 x + 1) \cdot \cos (x^{2} + 3 x + 1)

(\frac{d}{d x} (x^{2}) + \frac{d}{d x} (3 x) + 0) \cdot \cos (x^{2} + 3 x + 1)

ℹ

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

2 x

‖

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

3

(2 x + 3) \cdot \cos (x^{2} + 3 x + 1)

▶Derivative:

\cos (x^{2} + 3 x + 1) \cdot (2 x + 3)