Mister Exam

Derivative of y=sin3x-3sinx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(3*x) - 3*sin(x)
$$- 3 \sin{\left(x \right)} + \sin{\left(3 x \right)}$$
sin(3*x) - 3*sin(x)
Detail solution
  1. Differentiate term by term:

    1. Let .

    2. The derivative of sine is cosine:

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

      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:

      The result of the chain rule is:

    4. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of sine is cosine:

      So, the result is:

    The result is:


The answer is:

The graph
The first derivative [src]
-3*cos(x) + 3*cos(3*x)
$$- 3 \cos{\left(x \right)} + 3 \cos{\left(3 x \right)}$$
The second derivative [src]
3*(-3*sin(3*x) + sin(x))
$$3 \left(\sin{\left(x \right)} - 3 \sin{\left(3 x \right)}\right)$$
The third derivative [src]
3*(-9*cos(3*x) + cos(x))
$$3 \left(\cos{\left(x \right)} - 9 \cos{\left(3 x \right)}\right)$$
The graph
Derivative of y=sin3x-3sinx