Mister Exam

Derivative of sinxcos3x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(x)*cos(3*x)
$$\sin{\left(x \right)} \cos{\left(3 x \right)}$$
d                  
--(sin(x)*cos(3*x))
dx                 
$$\frac{d}{d x} \sin{\left(x \right)} \cos{\left(3 x \right)}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. The derivative of sine is cosine:

    ; to find :

    1. Let .

    2. The derivative of cosine is negative sine:

    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:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
cos(x)*cos(3*x) - 3*sin(x)*sin(3*x)
$$- 3 \sin{\left(x \right)} \sin{\left(3 x \right)} + \cos{\left(x \right)} \cos{\left(3 x \right)}$$
The second derivative [src]
-2*(3*cos(x)*sin(3*x) + 5*cos(3*x)*sin(x))
$$- 2 \cdot \left(5 \sin{\left(x \right)} \cos{\left(3 x \right)} + 3 \sin{\left(3 x \right)} \cos{\left(x \right)}\right)$$
The third derivative [src]
4*(-7*cos(x)*cos(3*x) + 9*sin(x)*sin(3*x))
$$4 \cdot \left(9 \sin{\left(x \right)} \sin{\left(3 x \right)} - 7 \cos{\left(x \right)} \cos{\left(3 x \right)}\right)$$
The graph
Derivative of sinxcos3x