Derivative of sin(4x+2)

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sin(4*x + 2)

$$\sin{\left(4 x + 2 \right)}$$

sin(4*x + 2)

Detail solution

Let $u = 4 x + 2$ .
The derivative of sine is cosine:

$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(4 x + 2\right)$ :
1. Differentiate $4 x + 2$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $4$
  2. The derivative of the constant $2$ is zero.
  The result is: $4$
The result of the chain rule is:

$4 \cos{\left(4 x + 2 \right)}$
Now simplify:

$4 \cos{\left(4 x + 2 \right)}$

The answer is:

$4 \cos{\left(4 x + 2 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

4*cos(4*x + 2)

$$4 \cos{\left(4 x + 2 \right)}$$

Simplify

The second derivative [src]

-16*sin(2*(1 + 2*x))

$$- 16 \sin{\left(2 \left(2 x + 1\right) \right)}$$

Simplify

The third derivative [src]

-64*cos(2*(1 + 2*x))

$$- 64 \cos{\left(2 \left(2 x + 1\right) \right)}$$

Simplify