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sqrt(x-1)
The derivative of the function/ sqrt(x-1)

Derivative of sqrt(x-1)

Function f() - derivative -N order at the point
v

The graph:

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The solution

You have entered [src] 
  _______
\/ x - 1
x−1\sqrt{x - 1} 
sqrt(x - 1)
Detail solution

  1. Let u=x−1u = x - 1.

  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−1)\frac{d}{d x} \left(x - 1\right):

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

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant −1-1 is zero.

      The result is: 11

    The result of the chain rule is:

    12x−1\frac{1}{2 \sqrt{x - 1}}

  4. Now simplify:

    12x−1\frac{1}{2 \sqrt{x - 1}}

The answer is:

12x−1\frac{1}{2 \sqrt{x - 1}}

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