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Derivative of:
Derivative of sin(4x)
Derivative of y=3x-2
Derivative of 2*x/(x-2)
Derivative of x^-5-4*x^-3+2*x-3
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)=(one /x)-x^(three)
f(x) equally (1 divide by x) minus x to the power of (3)
f(x) equally (one divide by x) minus x to the power of (three)
f(x)=(1/x)-x(3)
fx=1/x-x3
fx=1/x-x^3
f(x)=(1 divide by x)-x^(3)
Similar expressions
f(x)=(1/x)+x^(3)

The derivative of the function/ f(x)=(1/x)-x^(3)

Derivative of f(x)=(1/x)-x^(3)

The solution

You have entered [src]

1    3
- - x 
x

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

1/x - x^3

Detail solution

Differentiate $- x^{3} + \frac{1}{x}$ 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. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $- 3 x^{2}$
The result is: $- 3 x^{2} - \frac{1}{x^{2}}$
Now simplify:

$- \frac{3 x^{4} + 1}{x^{2}}$

The answer is:

$- \frac{3 x^{4} + 1}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

$$- 3 x^{2} - \frac{1}{x^{2}}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify