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Derivative of:
Derivative of f(x)=2x-3
Derivative of 2*cos(x)+sin(x)
Derivative of (1-x^2)^10
Derivative of (-1)/x+4*x^2
Identical expressions
(three x^- five)-(2x^-3)
(3x to the power of minus 5) minus (2x to the power of minus 3)
(three x to the power of minus five) minus (2x to the power of minus 3)
(3x-5)-(2x-3)
3x-5-2x-3
3x^-5-2x^-3
Similar expressions
(3x^+5)-(2x^-3)
(3x^-5)-(2x^+3)
(3x^-5)+(2x^-3)

The derivative of the function/ (3x^-5)-(2x^-3)

Derivative of (3x^-5)-(2x^-3)

The solution

You have entered [src]

3    2 
-- - --
 5    3
x    x

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

3/x^5 - 2/x^3

Detail solution

Differentiate $- \frac{2}{x^{3}} + \frac{3}{x^{5}}$ 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: $\frac{1}{x^{5}}$ goes to $- \frac{5}{x^{6}}$
  So, the result is: $- \frac{15}{x^{6}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $\frac{1}{x^{3}}$ goes to $- \frac{3}{x^{4}}$
  So, the result is: $\frac{6}{x^{4}}$
The result is: $\frac{6}{x^{4}} - \frac{15}{x^{6}}$
Now simplify:

$\frac{3 \left(2 x^{2} - 5\right)}{x^{6}}$

The answer is:

$\frac{3 \left(2 x^{2} - 5\right)}{x^{6}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  15   6 
- -- + --
   6    4
  x    x

$$\frac{6}{x^{4}} - \frac{15}{x^{6}}$$

Simplify

The second derivative [src]

  /     15\
6*|-4 + --|
  |      2|
  \     x /
-----------
      5    
     x

$$\frac{6 \left(-4 + \frac{15}{x^{2}}\right)}{x^{5}}$$

Simplify

The third derivative [src]

   /    21\
30*|4 - --|
   |     2|
   \    x /
-----------
      6    
     x

$$\frac{30 \left(4 - \frac{21}{x^{2}}\right)}{x^{6}}$$

Simplify