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The derivative of the function/ 3/x^2

Derivative of 3/x^2

The solution

You have entered [src]

3 
--
 2
x

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

3/x^2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x^{2}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$ :
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  The result of the chain rule is:
  
  $- \frac{2}{x^{3}}$
So, the result is: $- \frac{6}{x^{3}}$

The answer is:

$- \frac{6}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-6 
---
  3
 x

$$- \frac{6}{x^{3}}$$

Simplify

The second derivative [src]

18
--
 4
x

$$\frac{18}{x^{4}}$$

Simplify

The third derivative [src]

-72 
----
  5 
 x

$$- \frac{72}{x^{5}}$$

Simplify

The graph

Derivative of 3/x^2