Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x/(x+1)
Derivative of x/log(x)
Derivative of (x+1)/(x-1)
Derivative of (x^2-4)/x
Identical expressions
(seven *x- three)/(sqrt((x^ two)- five *x+ four))
(7 multiply by x minus 3) divide by ( square root of ((x squared ) minus 5 multiply by x plus 4))
(seven multiply by x minus three) divide by ( square root of ((x to the power of two) minus five multiply by x plus four))
(7*x-3)/(√((x^2)-5*x+4))
(7*x-3)/(sqrt((x2)-5*x+4))
7*x-3/sqrtx2-5*x+4
(7*x-3)/(sqrt((x²)-5*x+4))
(7*x-3)/(sqrt((x to the power of 2)-5*x+4))
(7x-3)/(sqrt((x^2)-5x+4))
(7x-3)/(sqrt((x2)-5x+4))
7x-3/sqrtx2-5x+4
7x-3/sqrtx^2-5x+4
(7*x-3) divide by (sqrt((x^2)-5*x+4))
Similar expressions
(7*x-3)/(sqrt((x^2)+5*x+4))
(7*x-3)/(sqrt((x^2)-5*x-4))
(7*x+3)/(sqrt((x^2)-5*x+4))

The derivative of the function/ (7*x-3)/(sqrt((x^2)-5*x+4))

Derivative of (7x-3)/(sqrt((x^2)-5x+4))

The solution

You have entered [src]

     7*x - 3     
-----------------
   ______________
  /  2           
\/  x  - 5*x + 4

$$\frac{7 x - 3}{\sqrt{x^{2} - 5 x + 4}}$$

d /     7*x - 3     \
--|-----------------|
dx|   ______________|
  |  /  2           |
  \\/  x  - 5*x + 4 /

$$\frac{d}{d x} \frac{7 x - 3}{\sqrt{x^{2} - 5 x + 4}}$$

Transform

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = 7 x - 3$ and $g{\left(x \right)} = \sqrt{x^{2} - 5 x + 4}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $7 x - 3$ 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: $7$
  The result is: $7$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Let $u = x^{2} - 5 x + 4$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 5 x + 4\right)$ :
  1. Differentiate $x^{2} - 5 x + 4$ term by term:
    1. The derivative of the constant $4$ is zero.
    2. Apply the power rule: $x^{2}$ goes to $2 x$
    3. 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: $-5$
    The result is: $2 x - 5$
  The result of the chain rule is:
  
  $\frac{2 x - 5}{2 \sqrt{x^{2} - 5 x + 4}}$
Now plug in to the quotient rule:

$\frac{- \frac{\left(2 x - 5\right) \left(7 x - 3\right)}{2 \sqrt{x^{2} - 5 x + 4}} + 7 \sqrt{x^{2} - 5 x + 4}}{x^{2} - 5 x + 4}$
Now simplify:

$\frac{41 - 29 x}{2 \left(x^{2} - 5 x + 4\right)^{\frac{3}{2}}}$

The answer is:

$\frac{41 - 29 x}{2 \left(x^{2} - 5 x + 4\right)^{\frac{3}{2}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        7           (-5/2 + x)*(7*x - 3)
----------------- - --------------------
   ______________                  3/2  
  /  2               / 2          \     
\/  x  - 5*x + 4     \x  - 5*x + 4/

$$- \frac{\left(x - \frac{5}{2}\right) \left(7 x - 3\right)}{\left(x^{2} - 5 x + 4\right)^{\frac{3}{2}}} + \frac{7}{\sqrt{x^{2} - 5 x + 4}}$$

Simplify

The second derivative [src]

            /                 2\           
            |     3*(-5 + 2*x) |           
            |-4 + -------------|*(-3 + 7*x)
            |           2      |           
            \      4 + x  - 5*x/           
35 - 14*x + -------------------------------
                           4               
-------------------------------------------
                           3/2             
             /     2      \                
             \4 + x  - 5*x/

$$\frac{- 14 x + \frac{\left(7 x - 3\right) \left(\frac{3 \left(2 x - 5\right)^{2}}{x^{2} - 5 x + 4} - 4\right)}{4} + 35}{\left(x^{2} - 5 x + 4\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

  /                        /                  2\                      \
  |                        |      5*(-5 + 2*x) |                      |
  |                        |-12 + -------------|*(-5 + 2*x)*(-3 + 7*x)|
  |                   2    |            2      |                      |
  |      21*(-5 + 2*x)     \       4 + x  - 5*x/                      |
3*|-7 + ---------------- - -------------------------------------------|
  |       /     2      \                   /     2      \             |
  \     4*\4 + x  - 5*x/                 8*\4 + x  - 5*x/             /
-----------------------------------------------------------------------
                                         3/2                           
                           /     2      \                              
                           \4 + x  - 5*x/

$$\frac{3 \cdot \left(\frac{21 \left(2 x - 5\right)^{2}}{4 \left(x^{2} - 5 x + 4\right)} - \frac{\left(2 x - 5\right) \left(7 x - 3\right) \left(\frac{5 \left(2 x - 5\right)^{2}}{x^{2} - 5 x + 4} - 12\right)}{8 \left(x^{2} - 5 x + 4\right)} - 7\right)}{\left(x^{2} - 5 x + 4\right)^{\frac{3}{2}}}$$

Simplify

The graph

Derivative of (7*x-3)/(sqrt((x^2)-5*x+4))

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of (7x-3)/(sqrt((x^2)-5x+4))

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of (7*x-3)/(sqrt((x^2)-5*x+4))

The graph:

Piecewise:

The solution

Derivative of (7x-3)/(sqrt((x^2)-5x+4))