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1/(sinx+cosx)

Derivative of 1/(sinx+cosx)

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

The graph:

from to

Piecewise:

The solution

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

  2. Apply the power rule: goes to

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

    1. Differentiate term by term:

      1. The derivative of sine is cosine:

      2. The derivative of cosine is negative sine:

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

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