Mister Exam

Derivative of (44x)-22tg(x)-(11п)-(11)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
44*x - 22*tan(x) - 11*pi - 11
$$\left(\left(44 x - 22 \tan{\left(x \right)}\right) - 11 \pi\right) - 11$$
44*x - 22*tan(x) - 11*pi - 11
Detail solution
  1. Differentiate term by term:

    1. Differentiate term by term:

      1. Differentiate term by term:

        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:

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

          1. Rewrite the function to be differentiated:

          2. Apply the quotient rule, which is:

            and .

            To find :

            1. The derivative of sine is cosine:

            To find :

            1. The derivative of cosine is negative sine:

            Now plug in to the quotient rule:

          So, the result is:

        The result is:

      2. The derivative of the constant is zero.

      The result is:

    2. The derivative of the constant is zero.

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
           2   
22 - 22*tan (x)
$$22 - 22 \tan^{2}{\left(x \right)}$$
The second derivative [src]
    /       2   \       
-44*\1 + tan (x)/*tan(x)
$$- 44 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}$$
The third derivative [src]
    /       2   \ /         2   \
-44*\1 + tan (x)/*\1 + 3*tan (x)/
$$- 44 \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 1\right)$$