Mister Exam

Derivative of coskx+sinkx.

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

The graph:

from to

Piecewise:

The solution

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

    1. Let .

    2. The derivative of cosine is negative sine:

    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:

    4. Let .

    5. The derivative of sine is cosine:

    6. 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:

  2. Now simplify:


The answer is:

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