Mister Exam

Derivative of y=sin2x*cos3x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(2*x)*cos(3*x)
$$\sin{\left(2 x \right)} \cos{\left(3 x \right)}$$
sin(2*x)*cos(3*x)
Detail solution
  1. Apply the product rule:

    ; 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:

    ; 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]
-3*sin(2*x)*sin(3*x) + 2*cos(2*x)*cos(3*x)
$$- 3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} + 2 \cos{\left(2 x \right)} \cos{\left(3 x \right)}$$
The second derivative [src]
-(12*cos(2*x)*sin(3*x) + 13*cos(3*x)*sin(2*x))
$$- (13 \sin{\left(2 x \right)} \cos{\left(3 x \right)} + 12 \sin{\left(3 x \right)} \cos{\left(2 x \right)})$$
The third derivative [src]
-62*cos(2*x)*cos(3*x) + 63*sin(2*x)*sin(3*x)
$$63 \sin{\left(2 x \right)} \sin{\left(3 x \right)} - 62 \cos{\left(2 x \right)} \cos{\left(3 x \right)}$$
The graph
Derivative of y=sin2x*cos3x