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Derivative of:
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Identical expressions
((x+ three)*exp(one))/(x- one)
((x plus 3) multiply by exponent of (1)) divide by (x minus 1)
((x plus three) multiply by exponent of (one)) divide by (x minus one)
((x+3)exp(1))/(x-1)
x+3exp1/x-1
((x+3)*exp(1)) divide by (x-1)
Similar expressions
((x+3)*exp(1))/(x+1)
((x-3)*exp(1))/(x-1)

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

Derivative of ((x+3)*exp(1))/(x-1)

The solution

You have entered [src]

         1
(x + 3)*e 
----------
  x - 1

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

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

Detail solution

Apply the quotient rule, which is:

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

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

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

    /    3 + x \
6*E*|1 - ------|
    \    -1 + x/
----------------
           3    
   (-1 + x)

$$\frac{6 e \left(1 - \frac{x + 3}{x - 1}\right)}{\left(x - 1\right)^{3}}$$

Simplify