Mister Exam

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

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

The graph:

from to

Piecewise:

The solution

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

    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:

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of sine is cosine:

      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 x*cos(x)-sin(x)