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Derivative of:
Derivative of tan(x/2)
Derivative of (x^2)
Derivative of sin(x)/2
Derivative of lnx
Graphing y =:
x^2/2+1/x
Identical expressions
x^ two / two + one /x
x squared divide by 2 plus 1 divide by x
x to the power of two divide by two plus one divide by x
x2/2+1/x
x²/2+1/x
x to the power of 2/2+1/x
x^2 divide by 2+1 divide by x
Similar expressions
x^2/2-1/x

The derivative of the function/ x^2/2+1/x

Derivative of x^2/2+1/x

The solution

You have entered [src]

 2    
x    1
-- + -
2    x

$$\frac{x^{2}}{2} + \frac{1}{x}$$

x^2/2 + 1/x

Detail solution

Differentiate $\frac{x^{2}}{2} + \frac{1}{x}$ 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: $x^{2}$ goes to $2 x$
  So, the result is: $x$
2. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
The result is: $x - \frac{1}{x^{2}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

Simplify

The second derivative [src]

$$1 + \frac{2}{x^{3}}$$

Simplify

3-я производная [src]

-6 
---
  4
 x

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

Simplify

The third derivative [src]

-6 
---
  4
 x

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

Simplify