Mister Exam

Derivative of tan(5*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
tan(5*x)
$$\tan{\left(5 x \right)}$$
d           
--(tan(5*x))
dx          
$$\frac{d}{d x} \tan{\left(5 x \right)}$$
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     
5 + 5*tan (5*x)
$$5 \tan^{2}{\left(5 x \right)} + 5$$
The second derivative [src]
   /       2     \         
50*\1 + tan (5*x)/*tan(5*x)
$$50 \left(\tan^{2}{\left(5 x \right)} + 1\right) \tan{\left(5 x \right)}$$
The third derivative [src]
    /       2     \ /         2     \
250*\1 + tan (5*x)/*\1 + 3*tan (5*x)/
$$250 \left(\tan^{2}{\left(5 x \right)} + 1\right) \left(3 \tan^{2}{\left(5 x \right)} + 1\right)$$
The graph
Derivative of tan(5*x)