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(three *x^ two - two)/x^ three
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(three multiply by x to the power of two minus two) divide by x to the power of three
(3*x2-2)/x3
3*x2-2/x3
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(3*x to the power of 2-2)/x to the power of 3
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(3*x^2-2) divide by x^3
Similar expressions
(3*x^2+2)/x^3
What you mean?
(3*x^2 - 1*2)/(x^3)
(3*x^2 - 1*2)*3/x
(3*x^2 - 1*2)/(x^3)
3*(x^2 - 1*2)/(x^3)
3*(x^2 - 1*2)*3/x
3*(x^2 - 1*2)/(x^3)
3*x^2 - 2/(x^3)

The derivative of the function/ (3*x^2-2)/x^3

You entered:

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

What you mean?

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

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

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

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

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

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

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

Derivative of (3*x^2-2)/x^3

The solution

You have entered [src]

   2    
3*x  - 2
--------
    3   
   x

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

  /   2    \
d |3*x  - 2|
--|--------|
dx|    3   |
  \   x    /

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

Transform

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = 3 x^{2} - 2$ and $g{\left(x \right)} = x^{3}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $3 x^{2} - 2$ term by term:
  1. The derivative of the constant $-2$ is zero.
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $6 x$
  The result is: $6 x$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
Now plug in to the quotient rule:

$\frac{6 x^{4} - 3 x^{2} \cdot \left(3 x^{2} - 2\right)}{x^{6}}$
Now simplify:

$\frac{3 \cdot \left(2 - x^{2}\right)}{x^{4}}$

The answer is:

$\frac{3 \cdot \left(2 - x^{2}\right)}{x^{4}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    /   2    \      
  3*\3*x  - 2/   6*x
- ------------ + ---
        4          3
       x          x

$$\frac{6 x}{x^{3}} - \frac{3 \cdot \left(3 x^{2} - 2\right)}{x^{4}}$$

Simplify

The second derivative [src]

  /       /        2\\
  |     2*\-2 + 3*x /|
6*|-5 + -------------|
  |            2     |
  \           x      /
----------------------
           3          
          x

$$\frac{6 \left(-5 + \frac{2 \cdot \left(3 x^{2} - 2\right)}{x^{2}}\right)}{x^{3}}$$

Simplify

The third derivative [src]

  /        /        2\\
  |     10*\-2 + 3*x /|
6*|27 - --------------|
  |            2      |
  \           x       /
-----------------------
            4          
           x

$$\frac{6 \cdot \left(27 - \frac{10 \cdot \left(3 x^{2} - 2\right)}{x^{2}}\right)}{x^{4}}$$

Simplify

The graph

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Derivative of (3*x^2-2)/x^3

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