Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of -e^x
Derivative of 1/2*sqrt(x)
Derivative of x-7
Derivative of x^5-5*x^3-20*x
Integral of d{x}:
1/(x^2-3*x+2)
Identical expressions
one /(x^ two - three *x+ two)
1 divide by (x squared minus 3 multiply by x plus 2)
one divide by (x to the power of two minus three multiply by x plus two)
1/(x2-3*x+2)
1/x2-3*x+2
1/(x²-3*x+2)
1/(x to the power of 2-3*x+2)
1/(x^2-3x+2)
1/(x2-3x+2)
1/x2-3x+2
1/x^2-3x+2
1 divide by (x^2-3*x+2)
Similar expressions
1/(x^2-3*x-2)
1/(x^2+3*x+2)

The derivative of the function/ 1/(x^2-3*x+2)

Derivative of 1/(x^2-3*x+2)

The solution

You have entered [src]

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

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

d /       1      \
--|1*------------|
dx|   2          |
  \  x  - 3*x + 2/

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

Transform

Detail solution

Apply the quotient rule, which is:

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

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

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of the constant $1$ is zero.
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x^{2} - 3 x + 2$ term by term:
  1. The derivative of the constant $2$ 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: $-3$
  The result is: $2 x - 3$
Now plug in to the quotient rule:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    3 - 2*x    
---------------
              2
/ 2          \ 
\x  - 3*x + 2/

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

              /               2 \
              |     (-3 + 2*x)  |
-6*(-3 + 2*x)*|-2 + ------------|
              |          2      |
              \     2 + x  - 3*x/
---------------------------------
                       3         
         /     2      \          
         \2 + x  - 3*x/

$$- \frac{6 \cdot \left(2 x - 3\right) \left(\frac{\left(2 x - 3\right)^{2}}{x^{2} - 3 x + 2} - 2\right)}{\left(x^{2} - 3 x + 2\right)^{3}}$$

Simplify

The graph

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of 1/(x^2-3*x+2)

The graph:

Piecewise:

The solution