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Derivative of:
Derivative of (1+x)/(4-x^2)
Derivative of (1+sqrt(x))/(1-sqrt(x))
Derivative of y=5-4x+7x³-x^5
Derivative of x/(x^2+4)
Identical expressions
(five -(one /x)+5x^- four)
(5 minus (1 divide by x) plus 5x to the power of minus 4)
(five minus (one divide by x) plus 5x to the power of minus four)
(5-(1/x)+5x-4)
5-1/x+5x-4
5-1/x+5x^-4
(5-(1 divide by x)+5x^-4)
Similar expressions
(5-(1/x)-5x^-4)
(5+(1/x)+5x^-4)
(5-(1/x)+5x^+4)

The derivative of the function/ (5-(1/x)+5x^-4)

Derivative of (5-(1/x)+5x^-4)

The solution

You have entered [src]

$$\left(5 - \frac{1}{x}\right) + \frac{5}{x^{4}}$$

5 - 1/x + 5/x^4

Detail solution

Differentiate $\left(5 - \frac{1}{x}\right) + \frac{5}{x^{4}}$ term by term:
1. Differentiate $5 - \frac{1}{x}$ term by term:
  1. The derivative of the constant $5$ is zero.
  2. 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: $\frac{1}{x^{2}}$
  The result is: $\frac{1}{x^{2}}$
2. 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: $- \frac{20}{x^{5}}$
The result is: $\frac{1}{x^{2}} - \frac{20}{x^{5}}$
Now simplify:

$\frac{x^{3} - 20}{x^{5}}$

The answer is:

$\frac{x^{3} - 20}{x^{5}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1    20
-- - --
 2    5
x    x

$$\frac{1}{x^{2}} - \frac{20}{x^{5}}$$

Simplify

The second derivative [src]

  /     50\
2*|-1 + --|
  |      3|
  \     x /
-----------
      3    
     x

$$\frac{2 \left(-1 + \frac{50}{x^{3}}\right)}{x^{3}}$$

Simplify

The third derivative [src]

  /    100\
6*|1 - ---|
  |      3|
  \     x /
-----------
      4    
     x

$$\frac{6 \left(1 - \frac{100}{x^{3}}\right)}{x^{4}}$$

Simplify