Mister Exam

Derivative of y=-tgx+2x-0,5пи+10

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
                pi     
-tan(x) + 2*x - -- + 10
                2      
$$2 x - \tan{\left(x \right)} - \frac{\pi}{2} + 10$$
d /                pi     \
--|-tan(x) + 2*x - -- + 10|
dx\                2      /
$$\frac{d}{d x} \left(2 x - \tan{\left(x \right)} - \frac{\pi}{2} + 10\right)$$
Detail solution
  1. Differentiate term by term:

    1. 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:

    2. 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:

    3. The derivative of the constant is zero.

    4. The derivative of the constant is zero.

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
       2   
1 - tan (x)
$$- \tan^{2}{\left(x \right)} + 1$$
The second derivative [src]
   /       2   \       
-2*\1 + tan (x)/*tan(x)
$$- 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}$$
The third derivative [src]
   /       2   \ /         2   \
-2*\1 + tan (x)/*\1 + 3*tan (x)/
$$- 2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 1\right)$$
The graph
Derivative of y=-tgx+2x-0,5пи+10