Derivative of 3x^-4

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3 
--
 4
x

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

3/x^4

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the power rule: $\frac{1}{x^{4}}$ goes to $- \frac{4}{x^{5}}$
So, the result is: $- \frac{12}{x^{5}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-12 
----
  5 
 x

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

Simplify

The second derivative [src]

60
--
 6
x

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

Simplify

The third derivative [src]

-360 
-----
   7 
  x

$$- \frac{360}{x^{7}}$$

Simplify

The graph