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Derivative of:
Derivative of e^(-x)
Derivative of e^x^2
Derivative of sin(x)/cos(x)
Derivative of cos(x)^(3)
Identical expressions
(y^(two)/ four)-(ln(y)/ two)
(y to the power of (2) divide by 4) minus (ln(y) divide by 2)
(y to the power of (two) divide by four) minus (ln(y) divide by two)
(y(2)/4)-(ln(y)/2)
y2/4-lny/2
y^2/4-lny/2
(y^(2) divide by 4)-(ln(y) divide by 2)
Similar expressions
(y^(2)/4)+(ln(y)/2)

The derivative of the function/ (y^(2)/4)-(ln(y)/2)

Derivative of (y^(2)/4)-(ln(y)/2)

The solution

You have entered [src]

 2         
y    log(y)
-- - ------
4      2

$$\frac{y^{2}}{4} - \frac{\log{\left(y \right)}}{2}$$

y^2/4 - log(y)/2

Detail solution

Differentiate $\frac{y^{2}}{4} - \frac{\log{\left(y \right)}}{2}$ 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: $y^{2}$ goes to $2 y$
  So, the result is: $\frac{y}{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $\log{\left(y \right)}$ is $\frac{1}{y}$ .
  So, the result is: $- \frac{1}{2 y}$
The result is: $\frac{y}{2} - \frac{1}{2 y}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

y    1 
- - ---
2   2*y

$$\frac{y}{2} - \frac{1}{2 y}$$

Simplify

The second derivative [src]

    1 
1 + --
     2
    y 
------
  2

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

Simplify

The third derivative [src]

-1 
---
  3
 y

$$- \frac{1}{y^{3}}$$

Simplify