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cos(sqrt(x))
The derivative of the function/ cos(sqrt(x))

Derivative of cos(sqrt(x))

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /  ___\
cos\\/ x /
$$\cos{\left(\sqrt{x} \right)}$$ 
d /   /  ___\\
--\cos\\/ x //
dx
$$\frac{d}{d x} \cos{\left(\sqrt{x} \right)}$$
Transform
Detail solution

  1. Let .

  2. The derivative of cosine is negative sine:

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

    1. Apply the power rule: goes to

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    /  ___\ 
-sin\\/ x / 
------------
      ___   
  2*\/ x
$$- \frac{\sin{\left(\sqrt{x} \right)}}{2 \sqrt{x}}$$
Simplify
The second derivative [src] 
   /  ___\      /  ___\
sin\\/ x /   cos\\/ x /
---------- - ----------
    3/2          x     
   x                   
-----------------------
           4
$$\frac{- \frac{\cos{\left(\sqrt{x} \right)}}{x} + \frac{\sin{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}}{4}$$
Simplify
The third derivative [src] 
   /  ___\        /  ___\        /  ___\
sin\\/ x /   3*sin\\/ x /   3*cos\\/ x /
---------- - ------------ + ------------
    3/2           5/2             2     
   x             x               x      
----------------------------------------
                   8
$$\frac{\frac{3 \cos{\left(\sqrt{x} \right)}}{x^{2}} + \frac{\sin{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} - \frac{3 \sin{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}}}}{8}$$
Simplify
The graph
Derivative of cos(sqrt(x))
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