Mister Exam

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The derivative of the function/ x^3/x

Derivative of x^3/x

The solution

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 3
x 
--
x

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

x^3/x

Detail solution

Apply the quotient rule, which is:

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

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

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
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:

$2 x$

The answer is:

$2 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2*x

$$2 x$$

Simplify

The second derivative [src]

$$2$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of x^3/x