Mister Exam

Derivative of tg^2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2   
tan (x)
$$\tan^{2}{\left(x \right)}$$
tan(x)^2
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    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:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
/         2   \       
\2 + 2*tan (x)/*tan(x)
$$\left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}$$
The second 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 third derivative [src]
  /       2   \ /         2   \       
8*\1 + tan (x)/*\2 + 3*tan (x)/*tan(x)
$$8 \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}$$
The graph
Derivative of tg^2x