Mister Exam

Derivative of tan(3*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
tan(3*x)
$$\tan{\left(3 x \right)}$$
tan(3*x)
Detail solution
  1. Rewrite the function to be differentiated:

  2. Apply the quotient rule, which is:

    and .

    To find :

    1. Let .

    2. The derivative of sine is cosine:

    3. 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:

    To find :

    1. Let .

    2. The derivative of cosine is negative sine:

    3. 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:

    Now plug in to the quotient rule:

  3. Now simplify:


The answer is:

The graph
The first derivative [src]
         2     
3 + 3*tan (3*x)
$$3 \tan^{2}{\left(3 x \right)} + 3$$
The second derivative [src]
   /       2     \         
18*\1 + tan (3*x)/*tan(3*x)
$$18 \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan{\left(3 x \right)}$$
The third derivative [src]
   /       2     \ /         2     \
54*\1 + tan (3*x)/*\1 + 3*tan (3*x)/
$$54 \left(\tan^{2}{\left(3 x \right)} + 1\right) \left(3 \tan^{2}{\left(3 x \right)} + 1\right)$$
The graph
Derivative of tan(3*x)