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Derivative of:
Derivative of x^-2
Derivative of x+3
Derivative of (-1)/x^2
Derivative of e^x^3
Identical expressions
y= three /x- one / three x^3
y equally 3 divide by x minus 1 divide by 3x cubed
y equally three divide by x minus one divide by three x cubed
y=3/x-1/3x3
y=3/x-1/3x³
y=3/x-1/3x to the power of 3
y=3 divide by x-1 divide by 3x^3
Similar expressions
y=3/x+1/3x^3

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

Derivative of y=3/x-1/3x^3

The solution

You have entered [src]

     3
3   x 
- - --
x   3

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

3/x - x^3/3

Detail solution

Differentiate $- \frac{x^{3}}{3} + \frac{3}{x}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
  So, the result is: $- \frac{3}{x^{2}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $- x^{2}$
The result is: $- x^{2} - \frac{3}{x^{2}}$
Now simplify:

$- \frac{x^{4} + 3}{x^{2}}$

The answer is:

$- \frac{x^{4} + 3}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

Simplify

The second derivative [src]

  /     3 \
2*|-x + --|
  |      3|
  \     x /

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

Simplify

The third derivative [src]

   /    9 \
-2*|1 + --|
   |     4|
   \    x /

$$- 2 \left(1 + \frac{9}{x^{4}}\right)$$

Simplify