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Graphing y =:
sqrt(x^2+16)
Identical expressions
sqrt(x^ two + sixteen)
square root of (x squared plus 16)
square root of (x to the power of two plus sixteen)
√(x^2+16)
sqrt(x2+16)
sqrtx2+16
sqrt(x²+16)
sqrt(x to the power of 2+16)
sqrtx^2+16
Similar expressions
sqrt(x^2-16)

The derivative of the function/ sqrt(x^2+16)

Derivative of sqrt(x^2+16)

The solution

You have entered [src]

   _________
  /  2      
\/  x  + 16

$$\sqrt{x^{2} + 16}$$

  /   _________\
d |  /  2      |
--\\/  x  + 16 /
dx

$$\frac{d}{d x} \sqrt{x^{2} + 16}$$

Transform

Detail solution

Let $u = x^{2} + 16$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} + 16\right)$ :
1. Differentiate $x^{2} + 16$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $16$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$\frac{x}{\sqrt{x^{2} + 16}}$
Now simplify:

$\frac{x}{\sqrt{x^{2} + 16}}$

The answer is:

$\frac{x}{\sqrt{x^{2} + 16}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     x      
------------
   _________
  /  2      
\/  x  + 16

$$\frac{x}{\sqrt{x^{2} + 16}}$$

Simplify

The second derivative [src]

        2   
       x    
1 - ------- 
          2 
    16 + x  
------------
   _________
  /       2 
\/  16 + x

$$\frac{- \frac{x^{2}}{x^{2} + 16} + 1}{\sqrt{x^{2} + 16}}$$

Simplify

The third derivative [src]

    /         2  \
    |        x   |
3*x*|-1 + -------|
    |           2|
    \     16 + x /
------------------
            3/2   
   /      2\      
   \16 + x /

$$\frac{3 x \left(\frac{x^{2}}{x^{2} + 16} - 1\right)}{\left(x^{2} + 16\right)^{\frac{3}{2}}}$$

Simplify

The graph

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Derivative of sqrt(x^2+16)

The graph:

Piecewise:

The solution