Mister Exam

Derivative of x+cos2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
x + cos(2*x)
$$x + \cos{\left(2 x \right)}$$
x + cos(2*x)
Detail solution
  1. Differentiate term by term:

    1. Apply the power rule: goes to

    2. Let .

    3. The derivative of cosine is negative sine:

    4. 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:


The answer is:

The graph
The first derivative [src]
1 - 2*sin(2*x)
$$1 - 2 \sin{\left(2 x \right)}$$
The second derivative [src]
-4*cos(2*x)
$$- 4 \cos{\left(2 x \right)}$$
The third derivative [src]
8*sin(2*x)
$$8 \sin{\left(2 x \right)}$$
The graph
Derivative of x+cos2x