Mister Exam

Derivative of tan(t)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
tan(t)
$$\tan{\left(t \right)}$$
tan(t)
Detail solution
  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. Now simplify:


The answer is:

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