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Derivative of:
Derivative of 2/sqrt(x)
Derivative of x*e^x^2
Derivative of x/cos(x)
Derivative of x*cot(x)
Identical expressions
y=sqrt(x^ two - two *x+ five)
y equally square root of (x squared minus 2 multiply by x plus 5)
y equally square root of (x to the power of two minus two multiply by x plus five)
y=√(x^2-2*x+5)
y=sqrt(x2-2*x+5)
y=sqrtx2-2*x+5
y=sqrt(x²-2*x+5)
y=sqrt(x to the power of 2-2*x+5)
y=sqrt(x^2-2x+5)
y=sqrt(x2-2x+5)
y=sqrtx2-2x+5
y=sqrtx^2-2x+5
Similar expressions
y=sqrt(x^2-2*x-5)
y=sqrt(x^2+2*x+5)

The derivative of the function/ y=sqrt(x^2-2*x+5)

Derivative of y=sqrt(x^2-2*x+5)

The solution

You have entered [src]

   ______________
  /  2           
\/  x  - 2*x + 5

$$\sqrt{x^{2} - 2 x + 5}$$

  /   ______________\
d |  /  2           |
--\\/  x  - 2*x + 5 /
dx

$$\frac{d}{d x} \sqrt{x^{2} - 2 x + 5}$$

Transform

Detail solution

Let $u = x^{2} - 2 x + 5$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 2 x + 5\right)$ :
1. Differentiate $x^{2} - 2 x + 5$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $2$
    So, the result is: $-2$
  3. The derivative of the constant $5$ is zero.
  The result is: $2 x - 2$
The result of the chain rule is:

$\frac{2 x - 2}{2 \sqrt{x^{2} - 2 x + 5}}$
Now simplify:

$\frac{x - 1}{\sqrt{x^{2} - 2 x + 5}}$

The answer is:

$\frac{x - 1}{\sqrt{x^{2} - 2 x + 5}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      -1 + x     
-----------------
   ______________
  /  2           
\/  x  - 2*x + 5

$$\frac{x - 1}{\sqrt{x^{2} - 2 x + 5}}$$

Simplify

The second derivative [src]

              2  
      (-1 + x)   
 1 - ------------
          2      
     5 + x  - 2*x
-----------------
   ______________
  /      2       
\/  5 + x  - 2*x

$$\frac{- \frac{\left(x - 1\right)^{2}}{x^{2} - 2 x + 5} + 1}{\sqrt{x^{2} - 2 x + 5}}$$

Simplify

The third derivative [src]

           /              2  \
           |      (-1 + x)   |
3*(-1 + x)*|-1 + ------------|
           |          2      |
           \     5 + x  - 2*x/
------------------------------
                    3/2       
      /     2      \          
      \5 + x  - 2*x/

$$\frac{3 \left(x - 1\right) \left(\frac{\left(x - 1\right)^{2}}{x^{2} - 2 x + 5} - 1\right)}{\left(x^{2} - 2 x + 5\right)^{\frac{3}{2}}}$$

Simplify

The graph

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Derivative of y=sqrt(x^2-2*x+5)

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The solution