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-(x^2+25)/x
The derivative of the function/ -(x^2+25)/x

Derivative of -(x^2+25)/x

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
   2     
- x  - 25
---------
    x
−x2−25x\frac{- x^{2} - 25}{x} 
(-x^2 - 25)/x
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)=−x2−25f{\left(x \right)} = - x^{2} - 25 and g(x)=xg{\left(x \right)} = x.

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

    1. Differentiate −x2−25- x^{2} - 25 term by term:

      1. The derivative of the constant −25-25 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: x2x^{2} goes to 2x2 x

        So, the result is: −2x- 2 x

      The result is: −2x- 2 x

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

    1. Apply the power rule: xx goes to 11

    Now plug in to the quotient rule:

    25−x2x2\frac{25 - x^{2}}{x^{2}}

  2. Now simplify:

    −1+25x2-1 + \frac{25}{x^{2}}

The answer is:

−1+25x2-1 + \frac{25}{x^{2}}

The graph
02468-8-6-4-2-10105000-2500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
        2     
     - x  - 25
-2 - ---------
          2   
         x
−2−−x2−25x2-2 - \frac{- x^{2} - 25}{x^{2}}
Simplify
The second derivative [src] 
  /          2\
  |    25 + x |
2*|1 - -------|
  |        2  |
  \       x   /
---------------
       x
2(1−x2+25x2)x\frac{2 \left(1 - \frac{x^{2} + 25}{x^{2}}\right)}{x}
Simplify
The third derivative [src] 
  /           2\
  |     25 + x |
6*|-1 + -------|
  |         2  |
  \        x   /
----------------
        2       
       x
6(−1+x2+25x2)x2\frac{6 \left(-1 + \frac{x^{2} + 25}{x^{2}}\right)}{x^{2}}
Simplify
The graph
Derivative of -(x^2+25)/x
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