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Identical expressions
one /x- three /x^ three
1 divide by x minus 3 divide by x cubed
one divide by x minus three divide by x to the power of three
1/x-3/x3
1/x-3/x³
1/x-3/x to the power of 3
1 divide by x-3 divide by x^3
Similar expressions
1/x+3/x^3

The derivative of the function/ 1/x-3/x^3

Derivative of 1/x-3/x^3

The solution

You have entered [src]

1   3 
- - --
x    3
    x

$$- \frac{3}{x^{3}} + \frac{1}{x}$$

1/x - 3/x^3

Detail solution

Differentiate $- \frac{3}{x^{3}} + \frac{1}{x}$ term by term:
1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = x^{3}$ .
  2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{3}$ :
    1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
    The result of the chain rule is:
    
    $- \frac{3}{x^{4}}$
  So, the result is: $\frac{9}{x^{4}}$
The result is: $- \frac{1}{x^{2}} + \frac{9}{x^{4}}$
Now simplify:

$\frac{9 - x^{2}}{x^{4}}$

The answer is:

$\frac{9 - x^{2}}{x^{4}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  1    9 
- -- + --
   2    4
  x    x

$$- \frac{1}{x^{2}} + \frac{9}{x^{4}}$$

Simplify

The second derivative [src]

  /    18\
2*|1 - --|
  |     2|
  \    x /
----------
     3    
    x

$$\frac{2 \left(1 - \frac{18}{x^{2}}\right)}{x^{3}}$$

Simplify

The third derivative [src]

  /     30\
6*|-1 + --|
  |      2|
  \     x /
-----------
      4    
     x

$$\frac{6 \left(-1 + \frac{30}{x^{2}}\right)}{x^{4}}$$

Simplify

The graph

Derivative of 1/x-3/x^3