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Derivative of:
Derivative of y=5
Derivative of x^3+1/x-1
Derivative of x^2*tgx
Derivative of sin(x-(3/5))-(8/5)
Factor polynomial:
x^3+1/x-1
Identical expressions
x^ three + one /x- one
x cubed plus 1 divide by x minus 1
x to the power of three plus one divide by x minus one
x3+1/x-1
x³+1/x-1
x to the power of 3+1/x-1
x^3+1 divide by x-1
Similar expressions
x^3-1/x-1
x^3+1/x+1

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

Derivative of x^3+1/x-1

The solution

You have entered [src]

 3   1    
x  + - - 1
     x

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

x^3 + 1/x - 1

Detail solution

Differentiate $\left(x^{3} + \frac{1}{x}\right) - 1$ term by term:
1. Differentiate $x^{3} + \frac{1}{x}$ term by term:
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  2. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
  The result is: $3 x^{2} - \frac{1}{x^{2}}$
2. The derivative of the constant $-1$ is zero.
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

The graph

Derivative of x^3+1/x-1