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Derivative of:
Derivative of 5/x^4
Derivative of sin^3t
Derivative of f(x)=3sinx+2cosx
Derivative of 5x^4+2x^3
Integral of d{x}:
5/x^4
Limit of the function:
5/x^4
Identical expressions
five /x^ four
5 divide by x to the power of 4
five divide by x to the power of four
5/x4
5/x⁴
5 divide by x^4

The derivative of the function/ 5/x^4

Derivative of 5/x^4

The solution

You have entered [src]

5 
--
 4
x

$$\frac{5}{x^{4}}$$

d /5 \
--|--|
dx| 4|
  \x /

$$\frac{d}{d x} \frac{5}{x^{4}}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x^{4}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{4}$ :
  1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  The result of the chain rule is:
  
  $- \frac{4}{x^{5}}$
So, the result is: $- \frac{20}{x^{5}}$

The answer is:

$- \frac{20}{x^{5}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-20 
----
  5 
 x

$$- \frac{20}{x^{5}}$$

Simplify

The second derivative [src]

100
---
  6
 x

$$\frac{100}{x^{6}}$$

Simplify

The third derivative [src]

-600 
-----
   7 
  x

$$- \frac{600}{x^{7}}$$

Simplify

The graph

Derivative of 5/x^4