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

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

Derivative of lnx-1/x^2

The solution

You have entered [src]

         1 
log(x) - --
          2
         x

$$\log{\left(x \right)} - \frac{1}{x^{2}}$$

log(x) - 1/x^2

Detail solution

Differentiate $\log{\left(x \right)} - \frac{1}{x^{2}}$ 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. Let $u = x^{2}$ .
  2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$ :
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    The result of the chain rule is:
    
    $- \frac{2}{x^{3}}$
  So, the result is: $\frac{2}{x^{3}}$
The result is: $\frac{1}{x} + \frac{2}{x^{3}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1   2 
- + --
x    3
    x

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

Simplify

The second derivative [src]

 /    6 \ 
-|1 + --| 
 |     2| 
 \    x / 
----------
     2    
    x

$$- \frac{1 + \frac{6}{x^{2}}}{x^{2}}$$

Simplify

The third derivative [src]

  /    12\
2*|1 + --|
  |     2|
  \    x /
----------
     3    
    x

$$\frac{2 \left(1 + \frac{12}{x^{2}}\right)}{x^{3}}$$

Simplify