Mister Exam

Derivative of y=sin(4x+3)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(4*x + 3)
$$\sin{\left(4 x + 3 \right)}$$
d               
--(sin(4*x + 3))
dx              
$$\frac{d}{d x} \sin{\left(4 x + 3 \right)}$$
Detail solution
  1. Let .

  2. The derivative of sine is cosine:

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate 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: goes to

        So, the result is:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
4*cos(4*x + 3)
$$4 \cos{\left(4 x + 3 \right)}$$
The second derivative [src]
-16*sin(3 + 4*x)
$$- 16 \sin{\left(4 x + 3 \right)}$$
The third derivative [src]
-64*cos(3 + 4*x)
$$- 64 \cos{\left(4 x + 3 \right)}$$
The graph
Derivative of y=sin(4x+3)