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sqrt(x-36)
The derivative of the function/ sqrt(x-36)

Derivative of sqrt(x-36)

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 - 36
x−36\sqrt{x - 36}
Transform
Detail solution

  1. Let u=x−36u = x - 36.

  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−36)\frac{d}{d x} \left(x - 36\right):

    1. Differentiate x−36x - 36 term by term:

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant −36-36 is zero.

      The result is: 11

    The result of the chain rule is:

    12x−36\frac{1}{2 \sqrt{x - 36}}

  4. Now simplify:

    12x−36\frac{1}{2 \sqrt{x - 36}}

The answer is:

12x−36\frac{1}{2 \sqrt{x - 36}}

The graph
02468-8-6-4-2-10100.02-0.02
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     1      
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    ________
2*\/ x - 36
12x−36\frac{1}{2 \sqrt{x - 36}}
Simplify
The second derivative [src] 
     -1       
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           3/2
4*(-36 + x)
−14(x−36)32- \frac{1}{4 \left(x - 36\right)^{\frac{3}{2}}}
Simplify
The third derivative [src] 
      3       
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           5/2
8*(-36 + x)
38(x−36)52\frac{3}{8 \left(x - 36\right)^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(x-36)
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