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Derivative of:
Derivative of (x^2-4)^3
Derivative of 7*x+5
Derivative of x/(x^4-3*x)
Derivative of log(x+3)-x
Identical expressions
lnx- one /8x^ two
lnx minus 1 divide by 8x squared
lnx minus one divide by 8x to the power of two
lnx-1/8x2
lnx-1/8x²
lnx-1/8x to the power of 2
lnx-1 divide by 8x^2
Similar expressions
lnx+1/8x^2

The derivative of the function/ lnx-1/8x^2

Derivative of lnx-1/8x^2

The solution

You have entered [src]

          2
         x 
log(x) - --
         8

$$- \frac{x^{2}}{8} + \log{\left(x \right)}$$

log(x) - x^2/8

Detail solution

Differentiate $- \frac{x^{2}}{8} + \log{\left(x \right)}$ term by term:
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
2. 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: $- \frac{x}{4}$
The result is: $- \frac{x}{4} + \frac{1}{x}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1   x
- - -
x   4

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

Simplify

The second derivative [src]

 /1   1 \
-|- + --|
 |4    2|
 \    x /

$$- (\frac{1}{4} + \frac{1}{x^{2}})$$

Simplify

The third derivative [src]

2 
--
 3
x

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

Simplify