Mister Exam

Derivative of y=sin2xcos2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(2*x)*cos(2*x)
$$\sin{\left(2 x \right)} \cos{\left(2 x \right)}$$
d                    
--(sin(2*x)*cos(2*x))
dx                   
$$\frac{d}{d x} \sin{\left(2 x \right)} \cos{\left(2 x \right)}$$
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:


The answer is:

The graph
The first derivative [src]
       2             2     
- 2*sin (2*x) + 2*cos (2*x)
$$- 2 \sin^{2}{\left(2 x \right)} + 2 \cos^{2}{\left(2 x \right)}$$
The second derivative [src]
-16*cos(2*x)*sin(2*x)
$$- 16 \sin{\left(2 x \right)} \cos{\left(2 x \right)}$$
The third derivative [src]
   /   2           2     \
32*\sin (2*x) - cos (2*x)/
$$32 \left(\sin^{2}{\left(2 x \right)} - \cos^{2}{\left(2 x \right)}\right)$$
The graph
Derivative of y=sin2xcos2x