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Derivative of:
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Identical expressions
(exp^ two (x- one))/(two (x- one))
( exponent of squared (x minus 1)) divide by (2(x minus 1))
( exponent of to the power of two (x minus one)) divide by (two (x minus one))
(exp2(x-1))/(2(x-1))
exp2x-1/2x-1
(exp²(x-1))/(2(x-1))
(exp to the power of 2(x-1))/(2(x-1))
exp^2x-1/2x-1
(exp^2(x-1)) divide by (2(x-1))
Similar expressions
(exp^2(x-1))/(2(x+1))
(exp^2(x+1))/(2(x-1))

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

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

The solution

You have entered [src]

 2        
e *(x - 1)
----------
2*(x - 1)

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

  / 2        \
d |e *(x - 1)|
--|----------|
dx\2*(x - 1) /

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

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. 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 $g{\left(x \right)} = 2 x - 2$ .
  
  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 $2 x - 2$ term by term:
    1. The derivative of the constant $-2$ 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:
  
  $0$
So, the result is: $0$

The answer is:

$0$

The first derivative [src]

                    2   
    1      2       e    
---------*e  - ---------
2*(x - 1)      2*(x - 1)

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

Simplify

The second derivative [src]

$$0$$

Simplify

The third derivative [src]

$$0$$

Simplify