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Derivative of:
Derivative of 4/x^3
Derivative of (x+3)^2*(x+5)-1
Derivative of x^3+2
Derivative of x^(-2)
Integral of d{x}:
4/x^3
Limit of the function:
4/x^3
Identical expressions
four /x^ three
4 divide by x cubed
four divide by x to the power of three
4/x3
4/x³
4/x to the power of 3
4 divide by x^3

The derivative of the function/ 4/x^3

Derivative of 4/x^3

The solution

You have entered [src]

4 
--
 3
x

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

4/x^3

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x^{3}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{3}$ :
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  The result of the chain rule is:
  
  $- \frac{3}{x^{4}}$
So, the result is: $- \frac{12}{x^{4}}$

The answer is:

$- \frac{12}{x^{4}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-12 
----
  4 
 x

$$- \frac{12}{x^{4}}$$

Simplify

The second derivative [src]

48
--
 5
x

$$\frac{48}{x^{5}}$$

Simplify

The third derivative [src]

-240 
-----
   6 
  x

$$- \frac{240}{x^{6}}$$

Simplify

The graph

Derivative of 4/x^3