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Derivative of:
Derivative of e^x^x
Derivative of ln(x+3)^3
Derivative of cos(3*x)^(2)
Derivative of -cos(2*x)
Graphing y =:
(x-1)^(1/2)
Integral of d{x}:
(x-1)^(1/2)
Identical expressions
(x- one)^(one / two)
(x minus 1) to the power of (1 divide by 2)
(x minus one) to the power of (one divide by two)
(x-1)(1/2)
x-11/2
x-1^1/2
(x-1)^(1 divide by 2)
Similar expressions
(x+1)^(1/2)

The derivative of the function/ (x-1)^(1/2)

Derivative of (x-1)^(1/2)

The solution

You have entered [src]

  _______
\/ x - 1

$$\sqrt{x - 1}$$

d /  _______\
--\\/ x - 1 /
dx

$$\frac{d}{d x} \sqrt{x - 1}$$

Transform

Detail solution

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

$\frac{1}{2 \sqrt{x - 1}}$
Now simplify:

$\frac{1}{2 \sqrt{x - 1}}$

The answer is:

$\frac{1}{2 \sqrt{x - 1}}$

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 (x-1)^(1/2)