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Derivative of:
Derivative of tan(x/2)
Derivative of (x^2)
Derivative of tan(x^3)
Derivative of sin(x)/2
Identical expressions
sqrt(x)+ four /sqrt(x)
square root of (x) plus 4 divide by square root of (x)
square root of (x) plus four divide by square root of (x)
√(x)+4/√(x)
sqrtx+4/sqrtx
sqrt(x)+4 divide by sqrt(x)
Similar expressions
sqrt(x)-4/sqrt(x)

The derivative of the function/ sqrt(x)+4/sqrt(x)

Derivative of sqrt(x)+4/sqrt(x)

The solution

You have entered [src]

  ___     4  
\/ x  + -----
          ___
        \/ x

$$\sqrt{x} + \frac{4}{\sqrt{x}}$$

sqrt(x) + 4/sqrt(x)

Detail solution

Differentiate $\sqrt{x} + \frac{4}{\sqrt{x}}$ term by term:
1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \sqrt{x}$ .
  2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{x}$ :
    1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
    The result of the chain rule is:
    
    $- \frac{1}{2 x^{\frac{3}{2}}}$
  So, the result is: $- \frac{2}{x^{\frac{3}{2}}}$
The result is: $\frac{1}{2 \sqrt{x}} - \frac{2}{x^{\frac{3}{2}}}$
Now simplify:

$\frac{x - 4}{2 x^{\frac{3}{2}}}$

The answer is:

$\frac{x - 4}{2 x^{\frac{3}{2}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1       2  
------- - ----
    ___    3/2
2*\/ x    x

$$\frac{1}{2 \sqrt{x}} - \frac{2}{x^{\frac{3}{2}}}$$

Simplify

The second derivative [src]

  1   3
- - + -
  4   x
-------
   3/2 
  x

$$\frac{- \frac{1}{4} + \frac{3}{x}}{x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

  /    20\
3*|1 - --|
  \    x /
----------
     5/2  
  8*x

$$\frac{3 \left(1 - \frac{20}{x}\right)}{8 x^{\frac{5}{2}}}$$

Simplify