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Derivative of:
Derivative of 4
Derivative of 1/x^3
Derivative of sin(x)^cos(x)
Derivative of ctgx-1
Integral of d{x}:
1/x^3
Graphing y =:
1/x^3
Identical expressions
one /x^ three
1 divide by x cubed
one divide by x to the power of three
1/x3
1/x³
1/x to the power of 3
1 divide by x^3
Similar expressions
x^1-1/x^3+x^(1/3)-2
1/(x^3+1)

The derivative of the function/ 1/x^3

Derivative of 1/x^3

The solution

You have entered [src]

  1 
1*--
   3
  x

$$1 \cdot \frac{1}{x^{3}}$$

d /  1 \
--|1*--|
dx|   3|
  \  x /

$$\frac{d}{d x} 1 \cdot \frac{1}{x^{3}}$$

Transform

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = 1$ and $g{\left(x \right)} = x^{3}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of the constant $1$ is zero.
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:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-3  
----
   3
x*x

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

Simplify

The second derivative [src]

12
--
 5
x

$$\frac{12}{x^{5}}$$

Simplify

The third derivative [src]

-60 
----
  6 
 x

$$- \frac{60}{x^{6}}$$

Simplify

The graph

Derivative of 1/x^3