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Derivative of:
Derivative of x^-6
Derivative of x^2*sqrt(1-x^2)
Derivative of x^3*cot(x)
Derivative of sin(x)+3
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)=(-3x+ five)/(2x- one)
f(x) equally ( minus 3x plus 5) divide by (2x minus 1)
f(x) equally ( minus 3x plus five) divide by (2x minus one)
fx=-3x+5/2x-1
f(x)=(-3x+5) divide by (2x-1)
Similar expressions
f(x)=(3x+5)/(2x-1)
f(x)=(-3x-5)/(2x-1)
f(x)=(-3x+5)/(2x+1)

The derivative of the function/ f(x)=(-3x+5)/(2x-1)

Derivative of f(x)=(-3x+5)/(2x-1)

The solution

You have entered [src]

-3*x + 5
--------
2*x - 1

$$\frac{5 - 3 x}{2 x - 1}$$

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

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = 5 - 3 x$ and $g{\left(x \right)} = 2 x - 1$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $5 - 3 x$ term by term:
  1. The derivative of the constant $5$ 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:

$- \frac{7}{\left(2 x - 1\right)^{2}}$

The answer is:

$- \frac{7}{\left(2 x - 1\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  /    2*(-5 + 3*x)\
4*|3 - ------------|
  \      -1 + 2*x  /
--------------------
              2     
    (-1 + 2*x)

$$\frac{4 \left(3 - \frac{2 \left(3 x - 5\right)}{2 x - 1}\right)}{\left(2 x - 1\right)^{2}}$$

Simplify

The third derivative [src]

   /     2*(-5 + 3*x)\
24*|-3 + ------------|
   \       -1 + 2*x  /
----------------------
               3      
     (-1 + 2*x)

$$\frac{24 \left(-3 + \frac{2 \left(3 x - 5\right)}{2 x - 1}\right)}{\left(2 x - 1\right)^{3}}$$

Simplify