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1/(sin(x))^2

Derivative of 1/(sin(x))^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   1   
-------
   2   
sin (x)
$$\frac{1}{\sin^{2}{\left(x \right)}}$$
1/(sin(x)^2)
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of sine is cosine:

      The result of the chain rule is:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
  -2*cos(x)   
--------------
          2   
sin(x)*sin (x)
$$- \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)} \sin^{2}{\left(x \right)}}$$
The second derivative [src]
  /         2   \
  |    3*cos (x)|
2*|1 + ---------|
  |        2    |
  \     sin (x) /
-----------------
        2        
     sin (x)     
$$\frac{2 \left(1 + \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right)}{\sin^{2}{\left(x \right)}}$$
The third derivative [src]
   /         2   \       
   |    3*cos (x)|       
-8*|2 + ---------|*cos(x)
   |        2    |       
   \     sin (x) /       
-------------------------
            3            
         sin (x)         
$$- \frac{8 \left(2 + \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{\sin^{3}{\left(x \right)}}$$
The graph
Derivative of 1/(sin(x))^2