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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
2x3−1⋅1x22 x^{3} - 1 \cdot \frac{1}{x^{2}} 
d /   3     1 \
--|2*x  - 1*--|
dx|          2|
  \         x /
ddx(2x3−1⋅1x2)\frac{d}{d x} \left(2 x^{3} - 1 \cdot \frac{1}{x^{2}}\right)
Transform
Detail solution

  1. Differentiate 2x3−1⋅1x22 x^{3} - 1 \cdot \frac{1}{x^{2}} 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: x3x^{3} goes to 3x23 x^{2}

      So, the result is: 6x26 x^{2}

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

      1. Let u=x2u = x^{2}.

      2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

      3. Then, apply the chain rule. Multiply by ddxx2\frac{d}{d x} x^{2}:

        1. Apply the power rule: x2x^{2} goes to 2x2 x

        The result of the chain rule is:

        −2x3- \frac{2}{x^{3}}

      So, the result is: 2x3\frac{2}{x^{3}}

    The result is: 6x2+2x36 x^{2} + \frac{2}{x^{3}}

  2. Now simplify:

    2⋅(3x5+1)x3\frac{2 \cdot \left(3 x^{5} + 1\right)}{x^{3}}

The answer is:

2⋅(3x5+1)x3\frac{2 \cdot \left(3 x^{5} + 1\right)}{x^{3}}

The graph
02468-8-6-4-2-1010-50005000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
2       2
-- + 6*x 
 3       
x
6x2+2x36 x^{2} + \frac{2}{x^{3}}
Simplify
The second derivative [src] 
  /  1       \
6*|- -- + 2*x|
  |   4      |
  \  x       /
6⋅(2x−1x4)6 \cdot \left(2 x - \frac{1}{x^{4}}\right)
Simplify
The third derivative [src] 
   /    2 \
12*|1 + --|
   |     5|
   \    x /
12⋅(1+2x5)12 \cdot \left(1 + \frac{2}{x^{5}}\right)
Simplify
The graph
Derivative of 2x³-1/x²
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