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Derivative of:
Derivative of cos(x/3)
Derivative of √x
Derivative of xcos(x)
Derivative of 50/x
Identical expressions
(two x^(2)+ fifty)/x
(2x to the power of (2) plus 50) divide by x
(two x to the power of (2) plus fifty) divide by x
(2x(2)+50)/x
2x2+50/x
2x^2+50/x
(2x^(2)+50) divide by x
Similar expressions
(2x^(2)-50)/x

The derivative of the function/ (2x^(2)+50)/x

Derivative of (2x^(2)+50)/x

The solution

You have entered [src]

   2     
2*x  + 50
---------
    x

$$\frac{2 x^{2} + 50}{x}$$

(2*x^2 + 50)/x

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = 2 x^{2} + 50$ and $g{\left(x \right)} = x$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $2 x^{2} + 50$ term by term:
  1. The derivative of the constant $50$ 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: $x^{2}$ goes to $2 x$
    So, the result is: $4 x$
  The result is: $4 x$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x$ goes to $1$
Now plug in to the quotient rule:

$\frac{2 x^{2} - 50}{x^{2}}$
Now simplify:

$2 - \frac{50}{x^{2}}$

The answer is:

$2 - \frac{50}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       2     
    2*x  + 50
4 - ---------
         2   
        x

$$4 - \frac{2 x^{2} + 50}{x^{2}}$$

Simplify

The second derivative [src]

  /           2\
  |     25 + x |
4*|-1 + -------|
  |         2  |
  \        x   /
----------------
       x

$$\frac{4 \left(-1 + \frac{x^{2} + 25}{x^{2}}\right)}{x}$$

Simplify

The third derivative [src]

   /          2\
   |    25 + x |
12*|1 - -------|
   |        2  |
   \       x   /
----------------
        2       
       x

$$\frac{12 \left(1 - \frac{x^{2} + 25}{x^{2}}\right)}{x^{2}}$$

Simplify