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Derivative of:
Derivative of sin(x)+cos(x)
Derivative of cos(x)^2
Derivative of sin(x^3)
Derivative of log(x)^2
Identical expressions
three /x- one /x^ four
3 divide by x minus 1 divide by x to the power of 4
three divide by x minus one divide by x to the power of four
3/x-1/x4
3/x-1/x⁴
3 divide by x-1 divide by x^4
Similar expressions
3/x+1/x^4

The derivative of the function/ 3/x-1/x^4

Derivative of 3/x-1/x^4

The solution

You have entered [src]

3   1 
- - --
x    4
    x

$$- \frac{1}{x^{4}} + \frac{3}{x}$$

3/x - 1/x^4

Detail solution

Differentiate $- \frac{1}{x^{4}} + \frac{3}{x}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
  So, the result is: $- \frac{3}{x^{2}}$
2. 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: $\frac{4}{x^{5}}$
The result is: $- \frac{3}{x^{2}} + \frac{4}{x^{5}}$
Now simplify:

$\frac{4 - 3 x^{3}}{x^{5}}$

The answer is:

$\frac{4 - 3 x^{3}}{x^{5}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  3    4 
- -- + --
   2    5
  x    x

$$- \frac{3}{x^{2}} + \frac{4}{x^{5}}$$

Simplify

The second derivative [src]

  /    10\
2*|3 - --|
  |     3|
  \    x /
----------
     3    
    x

$$\frac{2 \left(3 - \frac{10}{x^{3}}\right)}{x^{3}}$$

Simplify

The third derivative [src]

  /     20\
6*|-3 + --|
  |      3|
  \     x /
-----------
      4    
     x

$$\frac{6 \left(-3 + \frac{20}{x^{3}}\right)}{x^{4}}$$

Simplify

The graph

Derivative of 3/x-1/x^4