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Derivative of:
Derivative of (x^5+1)
Derivative of x^sqrt(x)
Derivative of log(x+2)
Derivative of ex^2
Identical expressions
(x- one)/(two *x- three)
(x minus 1) divide by (2 multiply by x minus 3)
(x minus one) divide by (two multiply by x minus three)
(x-1)/(2x-3)
x-1/2x-3
(x-1) divide by (2*x-3)
Similar expressions
(x+1)/(2*x-3)
(x-1)/(2*x+3)

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

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

The solution

You have entered [src]

 x - 1 
-------
2*x - 3

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

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

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x - 1$ and $g{\left(x \right)} = 2 x - 3$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x - 1$ term by term:
  1. The derivative of the constant $-1$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $2 x - 3$ 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. Apply the power rule: $x$ goes to $1$
    So, the result is: $2$
  The result is: $2$
Now plug in to the quotient rule:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  /     2*(-1 + x)\
4*|-1 + ----------|
  \      -3 + 2*x /
-------------------
              2    
    (-3 + 2*x)

$$\frac{4 \left(\frac{2 \left(x - 1\right)}{2 x - 3} - 1\right)}{\left(2 x - 3\right)^{2}}$$

Simplify

The third derivative [src]

   /    2*(-1 + x)\
24*|1 - ----------|
   \     -3 + 2*x /
-------------------
              3    
    (-3 + 2*x)

$$\frac{24 \left(- \frac{2 \left(x - 1\right)}{2 x - 3} + 1\right)}{\left(2 x - 3\right)^{3}}$$

Simplify