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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:

from to

Piecewise:

The solution

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

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     1     
-----------
    _______
2*\/ x - 1
$$\frac{1}{2 \sqrt{x - 1}}$$
Simplify
The second derivative [src] 
     -1      
-------------
          3/2
4*(-1 + x)
$$- \frac{1}{4 \left(x - 1\right)^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
      3      
-------------
          5/2
8*(-1 + x)
$$\frac{3}{8 \left(x - 1\right)^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of sqrt(x-1)
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