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

Derivative of sqrt(x+4)

Function f() - derivative -N order at the point
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The graph:

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The solution

You have entered [src] 
  _______
\/ x + 4
x+4\sqrt{x + 4} 
sqrt(x + 4)
Detail solution

  1. Let u=x+4u = x + 4.

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

  3. Then, apply the chain rule. Multiply by ddx(x+4)\frac{d}{d x} \left(x + 4\right):

    1. Differentiate x+4x + 4 term by term:

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant 44 is zero.

      The result is: 11

    The result of the chain rule is:

    12x+4\frac{1}{2 \sqrt{x + 4}}

  4. Now simplify:

    12x+4\frac{1}{2 \sqrt{x + 4}}

The answer is:

12x+4\frac{1}{2 \sqrt{x + 4}}

The graph
02468-8-6-4-2-101005
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     1     
-----------
    _______
2*\/ x + 4
12x+4\frac{1}{2 \sqrt{x + 4}}
Simplify
The second derivative [src] 
    -1      
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         3/2
4*(4 + x)
−14(x+4)32- \frac{1}{4 \left(x + 4\right)^{\frac{3}{2}}}
Simplify
The third derivative [src] 
     3      
------------
         5/2
8*(4 + x)
38(x+4)52\frac{3}{8 \left(x + 4\right)^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(x+4)
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