Mister Exam

Derivative of sin(x)-x*cos(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(x) - x*cos(x)
$$- x \cos{\left(x \right)} + \sin{\left(x \right)}$$
sin(x) - x*cos(x)
Detail solution
  1. Differentiate term by term:

    1. The derivative of sine is cosine:

    2. 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. Apply the power rule: goes to

        ; to find :

        1. The derivative of cosine is negative sine:

        The result is:

      So, the result is:

    The result is:


The answer is:

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