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Derivative of:
Derivative of sin(x)/cos(x)
Derivative of cos(x)^(3)
Derivative of tan(x^3)
Derivative of 1/(2*sqrt(x))
Graphing y =:
(x^4-3)/x
Identical expressions
(x^ four - three)/x
(x to the power of 4 minus 3) divide by x
(x to the power of four minus three) divide by x
(x4-3)/x
x4-3/x
(x⁴-3)/x
x^4-3/x
(x^4-3) divide by x
Similar expressions
(x^4+3)/x

The derivative of the function/ (x^4-3)/x

Derivative of (x^4-3)/x

The solution

You have entered [src]

 4    
x  - 3
------
  x

$$\frac{x^{4} - 3}{x}$$

(x^4 - 3)/x

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = x^{4} - 3$ and $g{\left(x \right)} = x$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{4} - 3$ term by term:
  1. The derivative of the constant $-3$ is zero.
  2. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  The result is: $4 x^{3}$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x$ goes to $1$
Now plug in to the quotient rule:

$\frac{3 x^{4} + 3}{x^{2}}$
Now simplify:

$\frac{3 \left(x^{4} + 1\right)}{x^{2}}$

The answer is:

$\frac{3 \left(x^{4} + 1\right)}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        4    
   2   x  - 3
4*x  - ------
          2  
         x

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify