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

Derivative of x^2/(x-3)

Function f() - derivative -N order at the point
v

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The solution

You have entered [src] 
   2 
  x  
-----
x - 3
x2x−3\frac{x^{2}}{x - 3} 
x^2/(x - 3)
Detail solution

  1. Apply the quotient rule, which is:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\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(x)=x2f{\left(x \right)} = x^{2} and g(x)=x−3g{\left(x \right)} = x - 3.

    To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: x2x^{2} goes to 2x2 x

    To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Differentiate x−3x - 3 term by term:

      1. The derivative of the constant −3-3 is zero.

      2. Apply the power rule: xx goes to 11

      The result is: 11

    Now plug in to the quotient rule:

    −x2+2x(x−3)(x−3)2\frac{- x^{2} + 2 x \left(x - 3\right)}{\left(x - 3\right)^{2}}

  2. Now simplify:

    x(x−6)(x−3)2\frac{x \left(x - 6\right)}{\left(x - 3\right)^{2}}

The answer is:

x(x−6)(x−3)2\frac{x \left(x - 6\right)}{\left(x - 3\right)^{2}}

The graph
02468-8-6-4-2-1010-20002000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      2           
     x        2*x 
- -------- + -----
         2   x - 3
  (x - 3)
−x2(x−3)2+2xx−3- \frac{x^{2}}{\left(x - 3\right)^{2}} + \frac{2 x}{x - 3}
Simplify
The second derivative [src] 
  /         2            \
  |        x        2*x  |
2*|1 + --------- - ------|
  |            2   -3 + x|
  \    (-3 + x)          /
--------------------------
          -3 + x
2(x2(x−3)2−2xx−3+1)x−3\frac{2 \left(\frac{x^{2}}{\left(x - 3\right)^{2}} - \frac{2 x}{x - 3} + 1\right)}{x - 3}
Simplify
The third derivative [src] 
  /          2            \
  |         x        2*x  |
6*|-1 - --------- + ------|
  |             2   -3 + x|
  \     (-3 + x)          /
---------------------------
                 2         
         (-3 + x)
6(−x2(x−3)2+2xx−3−1)(x−3)2\frac{6 \left(- \frac{x^{2}}{\left(x - 3\right)^{2}} + \frac{2 x}{x - 3} - 1\right)}{\left(x - 3\right)^{2}}
Simplify
The graph
Derivative of x^2/(x-3)
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