Mister Exam

Lang:

Other calculators

How to use it?
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 plus 1 divide by x squared
lnx plus 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. Let $u = x^{2}$ .
3. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
4. 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:
  
  $- \frac{2}{x^{3}}$
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      2
    x*x

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

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