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Derivative of e^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                  
E *(cos(x) - sin(x))
$$e^{x} \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
E^x*(cos(x) - sin(x))
Detail solution
  1. Apply the product rule:

    ; to find :

    1. The derivative of is itself.

    ; to find :

    1. Differentiate term by term:

      1. The derivative of cosine is negative sine:

      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 result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
                    x                      x
(-cos(x) - sin(x))*e  + (cos(x) - sin(x))*e 
$$\left(- \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x} + \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) e^{x}$$
The second derivative [src]
                      x
-2*(cos(x) + sin(x))*e 
$$- 2 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) e^{x}$$
3-я производная [src]
           x
-4*cos(x)*e 
$$- 4 e^{x} \cos{\left(x \right)}$$
The third derivative [src]
           x
-4*cos(x)*e 
$$- 4 e^{x} \cos{\left(x \right)}$$