Mister Exam

Derivative of csc(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
csc(x)
$$\csc{\left(x \right)}$$
csc(x)
Detail solution
  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. The derivative of sine is cosine:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
-cot(x)*csc(x)
$$- \cot{\left(x \right)} \csc{\left(x \right)}$$
The second derivative [src]
/         2   \       
\1 + 2*cot (x)/*csc(x)
$$\left(2 \cot^{2}{\left(x \right)} + 1\right) \csc{\left(x \right)}$$
The third derivative [src]
 /         2   \              
-\5 + 6*cot (x)/*cot(x)*csc(x)
$$- \left(6 \cot^{2}{\left(x \right)} + 5\right) \cot{\left(x \right)} \csc{\left(x \right)}$$
The graph
Derivative of csc(x)