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Derivative of 1/cos^2y

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   1   
-------
   2   
cos (y)
$$\frac{1}{\cos^{2}{\left(y \right)}}$$
1/(cos(y)^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 cosine is negative sine:

      The result of the chain rule is:

    The result of the chain rule is:


The answer is:

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