Mister Exam

Derivative of tanx/2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
tan(x)
------
  2   
$$\frac{\tan{\left(x \right)}}{2}$$
tan(x)/2
Detail solution
  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. Now simplify:


The answer is:

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