Mister Exam

Derivative of y=sin(2x)cos(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(2*x)*cos(x)
$$\sin{\left(2 x \right)} \cos{\left(x \right)}$$
d                  
--(sin(2*x)*cos(x))
dx                 
$$\frac{d}{d x} \sin{\left(2 x \right)} \cos{\left(x \right)}$$
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. The derivative of cosine is negative sine:

    The result is:

  2. Now simplify:


The answer is:

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