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(-1)/cos(x)
The derivative of the function/ (-1)/cos(x)

Derivative of (-1)/cos(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 -1   
------
cos(x)
$$- \frac{1}{\cos{\left(x \right)}}$$ 
-1/cos(x)
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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:

    So, the result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-sin(x) 
--------
   2    
cos (x)
$$- \frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}$$
Simplify
The second derivative [src] 
 /         2   \ 
 |    2*sin (x)| 
-|1 + ---------| 
 |        2    | 
 \     cos (x) / 
-----------------
      cos(x)
$$- \frac{\frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1}{\cos{\left(x \right)}}$$
Simplify
The third derivative [src] 
 /         2   \        
 |    6*sin (x)|        
-|5 + ---------|*sin(x) 
 |        2    |        
 \     cos (x) /        
------------------------
           2            
        cos (x)
$$- \frac{\left(\frac{6 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 5\right) \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}$$
Simplify
The graph
Derivative of (-1)/cos(x)
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