Mister Exam

Derivative of ctg(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
cot(x)
$$\cot{\left(x \right)}$$
d         
--(cot(x))
dx        
$$\frac{d}{d x} \cot{\left(x \right)}$$
Detail solution
  1. There are multiple ways to do this derivative.

    Method #1

    1. Rewrite the function to be differentiated:

    2. Let .

    3. Apply the power rule: goes to

    4. 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:

    Method #2

    1. Rewrite the function to be differentiated:

    2. Apply the quotient rule, which is:

      and .

      To find :

      1. The derivative of cosine is negative sine:

      To find :

      1. The derivative of sine is cosine:

      Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

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