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Derivative of:
Derivative of 4/x^3
Derivative of (x+3)^2*(x+5)-1
Derivative of x^3+2
Derivative of x^(-2)
Graphing y =:
sqrt(4+x^2)
Integral of d{x}:
sqrt(4+x^2)
Limit of the function:
sqrt(4+x^2)
Identical expressions
sqrt(four +x^ two)
square root of (4 plus x squared )
square root of (four plus x to the power of two)
√(4+x^2)
sqrt(4+x2)
sqrt4+x2
sqrt(4+x²)
sqrt(4+x to the power of 2)
sqrt4+x^2
Similar expressions
sqrt(4-x^2)
(x^2-6)*sqrt((4+x^2))/120x

The derivative of the function/ sqrt(4+x^2)

Derivative of sqrt(4+x^2)

The solution

You have entered [src]

   ________
  /      2 
\/  4 + x

$$\sqrt{x^{2} + 4}$$

sqrt(4 + x^2)

Detail solution

Let $u = x^{2} + 4$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} + 4\right)$ :
1. Differentiate $x^{2} + 4$ term by term:
  1. The derivative of the constant $4$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  The result is: $2 x$
The result of the chain rule is:

$\frac{x}{\sqrt{x^{2} + 4}}$

The answer is:

$\frac{x}{\sqrt{x^{2} + 4}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     x     
-----------
   ________
  /      2 
\/  4 + x

$$\frac{x}{\sqrt{x^{2} + 4}}$$

Simplify

The second derivative [src]

        2  
       x   
 1 - ------
          2
     4 + x 
-----------
   ________
  /      2 
\/  4 + x

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

Simplify

The third derivative [src]

    /        2  \
    |       x   |
3*x*|-1 + ------|
    |          2|
    \     4 + x /
-----------------
           3/2   
   /     2\      
   \4 + x /

$$\frac{3 x \left(\frac{x^{2}}{x^{2} + 4} - 1\right)}{\left(x^{2} + 4\right)^{\frac{3}{2}}}$$

Simplify

The graph

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Identical expressions

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Derivative of sqrt(4+x^2)

The graph:

Piecewise:

The solution