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y=(e^1-3x)/(2x-1)

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Identical expressions
y=(e^ one -3x)/(2x- one)
y equally (e to the power of 1 minus 3x) divide by (2x minus 1)
y equally (e to the power of one minus 3x) divide by (2x minus one)
y=(e1-3x)/(2x-1)
y=e1-3x/2x-1
y=e^1-3x/2x-1
y=(e^1-3x) divide by (2x-1)
Similar expressions
y=(e^1-3x)/(2x+1)
y=(e^1+3x)/(2x-1)

The derivative of the function/ y=(e^1-3x)/(2x-1)

Derivative of y=(e^1-3x)/(2x-1)

The solution

You have entered [src]

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

$$\frac{- 3 x + e^{1}}{2 x - 1}$$

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

Detail solution

Apply the quotient rule, which is:

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

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

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $e - 3 x$ term by term:
  1. The derivative of the constant $e$ 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: $-3$
  The result is: $-3$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $2 x - 1$ term by term:
  1. The derivative of the constant $-1$ 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:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of y=(e^1-3x)/(2x-1)