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Graphing y =:
x^2/(x-4)
How do you in partial fractions?:
x^2/(x-4)
Identical expressions
x^ two /(x- four)
x squared divide by (x minus 4)
x to the power of two divide by (x minus four)
x2/(x-4)
x2/x-4
x²/(x-4)
x to the power of 2/(x-4)
x^2/x-4
x^2 divide by (x-4)
Similar expressions
x^2/(x+4)

The derivative of the function/ x^2/(x-4)

Derivative of x^2/(x-4)

The solution

You have entered [src]

   2 
  x  
-----
x - 4

$$\frac{x^{2}}{x - 4}$$

x^2/(x - 4)

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = x^{2}$ and $g{\left(x \right)} = x - 4$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x - 4$ term by term:
  1. The derivative of the constant $-4$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
Now plug in to the quotient rule:

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

$\frac{x \left(x - 8\right)}{\left(x - 4\right)^{2}}$

The answer is:

$\frac{x \left(x - 8\right)}{\left(x - 4\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      2           
     x        2*x 
- -------- + -----
         2   x - 4
  (x - 4)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

  /          2            \
  |         x        2*x  |
6*|-1 - --------- + ------|
  |             2   -4 + x|
  \     (-4 + x)          /
---------------------------
                 2         
         (-4 + x)

$$\frac{6 \left(- \frac{x^{2}}{\left(x - 4\right)^{2}} + \frac{2 x}{x - 4} - 1\right)}{\left(x - 4\right)^{2}}$$

Simplify

The graph

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Derivative of x^2/(x-4)

The graph:

Piecewise:

The solution