Mister Exam

Derivative of y=(xsinx)+(cosx)

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

The graph:

from to

Piecewise:

The solution

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

      The result is:

    2. The derivative of cosine is negative sine:

    The result is:


The answer is:

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