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Derivative of cos(x)-sqrt(x+2)-1

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
           _______    
cos(x) - \/ x + 2  - 1
$$\left(- \sqrt{x + 2} + \cos{\left(x \right)}\right) - 1$$
cos(x) - sqrt(x + 2) - 1
Detail solution
  1. Differentiate term by term:

    1. Differentiate term by term:

      1. The derivative of cosine is negative sine:

      2. 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. Differentiate term by term:

            1. Apply the power rule: goes to

            2. The derivative of the constant is zero.

            The result is:

          The result of the chain rule is:

        So, the result is:

      The result is:

    2. The derivative of the constant is zero.

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
               1     
-sin(x) - -----------
              _______
          2*\/ x + 2 
$$- \sin{\left(x \right)} - \frac{1}{2 \sqrt{x + 2}}$$
The second derivative [src]
               1      
-cos(x) + ------------
                   3/2
          4*(2 + x)   
$$- \cos{\left(x \right)} + \frac{1}{4 \left(x + 2\right)^{\frac{3}{2}}}$$
The third derivative [src]
       3               
- ------------ + sin(x)
           5/2         
  8*(2 + x)            
$$\sin{\left(x \right)} - \frac{3}{8 \left(x + 2\right)^{\frac{5}{2}}}$$