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Derivative of sqrt(x)+2*cosx

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

The graph:

from to

Piecewise:

The solution

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

    1. Apply the power rule: goes to

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

      1. The derivative of cosine is negative sine:

      So, the result is:

    The result is:


The answer is:

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