Mister Exam

Derivative of 3sin2x*cosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
3*sin(2*x)*cos(x)
$$3 \sin{\left(2 x \right)} \cos{\left(x \right)}$$
d                    
--(3*sin(2*x)*cos(x))
dx                   
$$\frac{d}{d x} 3 \sin{\left(2 x \right)} \cos{\left(x \right)}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Apply the product rule:

      ; to find :

      1. The derivative of cosine is negative sine:

      ; to find :

      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:

      The result is:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
-3*sin(x)*sin(2*x) + 6*cos(x)*cos(2*x)
$$- 3 \sin{\left(x \right)} \sin{\left(2 x \right)} + 6 \cos{\left(x \right)} \cos{\left(2 x \right)}$$
The second derivative [src]
-3*(4*cos(2*x)*sin(x) + 5*cos(x)*sin(2*x))
$$- 3 \cdot \left(4 \sin{\left(x \right)} \cos{\left(2 x \right)} + 5 \sin{\left(2 x \right)} \cos{\left(x \right)}\right)$$
The third derivative [src]
3*(-14*cos(x)*cos(2*x) + 13*sin(x)*sin(2*x))
$$3 \cdot \left(13 \sin{\left(x \right)} \sin{\left(2 x \right)} - 14 \cos{\left(x \right)} \cos{\left(2 x \right)}\right)$$
The graph
Derivative of 3sin2x*cosx