Mister Exam

Derivative of tg(x)-9*x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
tan(x) - 9*x
$$- 9 x + \tan{\left(x \right)}$$
tan(x) - 9*x
Detail solution
  1. Differentiate term by term:

    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:

    3. 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 is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
        2   
-8 + tan (x)
$$\tan^{2}{\left(x \right)} - 8$$
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)/
$$2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 1\right)$$