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Derivative of (x^2+1)^3
Derivative of cos(x)^(3)
Graphing y =:
(x^2+5)/(x-3)
Identical expressions
(x^ two + five)/(x- three)
(x squared plus 5) divide by (x minus 3)
(x to the power of two plus five) divide by (x minus three)
(x2+5)/(x-3)
x2+5/x-3
(x²+5)/(x-3)
(x to the power of 2+5)/(x-3)
x^2+5/x-3
(x^2+5) divide by (x-3)
Similar expressions
(x^2+5)/(x+3)
(x^2-5)/(x-3)

The derivative of the function/ (x^2+5)/(x-3)

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

The solution

You have entered [src]

 2    
x  + 5
------
x - 3

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

(x^2 + 5)/(x - 3)

Detail solution

Apply the quotient rule, which is:

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

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    2             
   x  + 5     2*x 
- -------- + -----
         2   x - 3
  (x - 3)

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

Simplify

The second derivative [src]

  /           2          \
  |      5 + x      2*x  |
2*|1 + --------- - ------|
  |            2   -3 + x|
  \    (-3 + x)          /
--------------------------
          -3 + x

$$\frac{2 \left(- \frac{2 x}{x - 3} + 1 + \frac{x^{2} + 5}{\left(x - 3\right)^{2}}\right)}{x - 3}$$

Simplify

3-я производная [src]

  /            2          \
  |       5 + x      2*x  |
6*|-1 - --------- + ------|
  |             2   -3 + x|
  \     (-3 + x)          /
---------------------------
                 2         
         (-3 + x)

$$\frac{6 \left(\frac{2 x}{x - 3} - 1 - \frac{x^{2} + 5}{\left(x - 3\right)^{2}}\right)}{\left(x - 3\right)^{2}}$$

Simplify

The third derivative [src]

  /            2          \
  |       5 + x      2*x  |
6*|-1 - --------- + ------|
  |             2   -3 + x|
  \     (-3 + x)          /
---------------------------
                 2         
         (-3 + x)

$$\frac{6 \left(\frac{2 x}{x - 3} - 1 - \frac{x^{2} + 5}{\left(x - 3\right)^{2}}\right)}{\left(x - 3\right)^{2}}$$

Simplify

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

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Piecewise:

The solution