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Derivative of:
Derivative of 3*sqrt(x)
Derivative of 2*y
Derivative of 2^x+1
Derivative of (2x-1)^3
Graphing y =:
1/(sinx+cosx)
Integral of d{x}:
1/(sinx+cosx)
Identical expressions
one /(sinx+cosx)
1 divide by ( sinus of x plus co sinus of e of x)
one divide by ( sinus of x plus co sinus of e of x)
1/sinx+cosx
1 divide by (sinx+cosx)
Similar expressions
1/((sin(x)+cos(x))^2)
1/(sinx-cosx)

The derivative of the function/ 1/(sinx+cosx)

Derivative of 1/(sinx+cosx)

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

Let $u = \sin{\left(x \right)} + \cos{\left(x \right)}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)$ :
1. Differentiate $\sin{\left(x \right)} + \cos{\left(x \right)}$ term by term:
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  2. The derivative of cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  The result is: $- \sin{\left(x \right)} + \cos{\left(x \right)}$
The result of the chain rule is:

$- \frac{- \sin{\left(x \right)} + \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}$
Now simplify:

$- \frac{\sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}}{\sin{\left(2 x \right)} + 1}$

The answer is:

$- \frac{\sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}}{\sin{\left(2 x \right)} + 1}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 -cos(x) + sin(x) 
------------------
                 2
(sin(x) + cos(x))

$$\frac{\sin{\left(x \right)} - \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}$$

Simplify

The second derivative [src]

                        2
    2*(-cos(x) + sin(x)) 
1 + ---------------------
                       2 
      (cos(x) + sin(x))  
-------------------------
     cos(x) + sin(x)

$$\frac{\frac{2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}} + 1}{\sin{\left(x \right)} + \cos{\left(x \right)}}$$

Simplify

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))

$$\frac{\left(\frac{6 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}} + 5\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}$$

Simplify

The graph

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Derivative of 1/(sinx+cosx)

The graph:

Piecewise:

The solution