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Derivative of:
Derivative of x+3
Derivative of sqrt(x^2+1)
Derivative of 1/sin(x)
Derivative of x^x^2
Identical expressions
three -sqrt(two *x- one)
3 minus square root of (2 multiply by x minus 1)
three minus square root of (two multiply by x minus one)
3-√(2*x-1)
3-sqrt(2x-1)
3-sqrt2x-1
Similar expressions
3+sqrt(2*x-1)
3-sqrt(2*x+1)

The derivative of the function/ 3-sqrt(2*x-1)

Derivative of 3-sqrt(2*x-1)

The solution

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      _________
3 - \/ 2*x - 1

$$3 - \sqrt{2 x - 1}$$

3 - sqrt(2*x - 1)

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    -1     
-----------
  _________
\/ 2*x - 1

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

Simplify

The second derivative [src]

      1      
-------------
          3/2
(-1 + 2*x)

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

Simplify

The third derivative [src]

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

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

Simplify