Mister Exam

Derivative of y*sin(2*y)

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

The graph:

from to

Piecewise:

The solution

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

    ; to find :

    1. Apply the power rule: goes to

    ; 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:


The answer is:

The graph
The first derivative [src]
2*y*cos(2*y) + sin(2*y)
$$2 y \cos{\left(2 y \right)} + \sin{\left(2 y \right)}$$
The second derivative [src]
4*(-y*sin(2*y) + cos(2*y))
$$4 \left(- y \sin{\left(2 y \right)} + \cos{\left(2 y \right)}\right)$$
The third derivative [src]
-4*(3*sin(2*y) + 2*y*cos(2*y))
$$- 4 \left(2 y \cos{\left(2 y \right)} + 3 \sin{\left(2 y \right)}\right)$$
The graph
Derivative of y*sin(2*y)