Mister Exam

Other calculators

2x³-1/x²
The derivative of the function/ 2x³-1/x²

You entered:

2x³-1/x²

What you mean?

(2*x^3 - 1*1)/(x^2)
 
(2*x^3 - 1*1)*2/x
 
(2*x^3 - 1*1)/(x^2)
 
2*(x^3 - 1*1)/(x^2)
 
2*(x^3 - 1*1)*2/x
 
2*(x^3 - 1*1)/(x^2)
 
2*x^3 - 1/(x^2)

Derivative of 2x³-1/x²

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   3     1 
2*x  - 1*--
          2
         x
$$2 x^{3} - 1 \cdot \frac{1}{x^{2}}$$ 
d /   3     1 \
--|2*x  - 1*--|
dx|          2|
  \         x /
$$\frac{d}{d x} \left(2 x^{3} - 1 \cdot \frac{1}{x^{2}}\right)$$
Transform
Detail solution

  1. Differentiate 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: goes to

      So, the result is:

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Let .

      2. Apply the power rule: goes to

      3. Then, apply the chain rule. Multiply by :

        1. Apply the power rule: goes to

        The result of the chain rule is:

      So, the result is:

    The result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
2       2
-- + 6*x 
 3       
x
$$6 x^{2} + \frac{2}{x^{3}}$$
Simplify
The second derivative [src] 
  /  1       \
6*|- -- + 2*x|
  |   4      |
  \  x       /
$$6 \cdot \left(2 x - \frac{1}{x^{4}}\right)$$
Simplify
The third derivative [src] 
   /    2 \
12*|1 + --|
   |     5|
   \    x /
$$12 \cdot \left(1 + \frac{2}{x^{5}}\right)$$
Simplify
The graph
Derivative of 2x³-1/x²
    © Mister Exam – Calculator