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Derivative of:
Derivative of asin(x)
Derivative of cos(x^3)
Derivative of (cos(x))^3
Derivative of 1/tan(x)
Graphing y =:
x^2-ln(x^2)
Identical expressions
x^ two -ln(x^ two)
x squared minus ln(x squared )
x to the power of two minus ln(x to the power of two)
x2-ln(x2)
x2-lnx2
x²-ln(x²)
x to the power of 2-ln(x to the power of 2)
x^2-lnx^2
Similar expressions
x^2+ln(x^2)

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

Derivative of x^2-ln(x^2)

The solution

You have entered [src]

 2      / 2\
x  - log\x /

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

x^2 - log(x^2)

Detail solution

Differentiate $x^{2} - \log{\left(x^{2} \right)}$ term by term:
1. Apply the power rule: $x^{2}$ goes to $2 x$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = x^{2}$ .
  2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
  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:
    
    $\frac{2}{x}$
  So, the result is: $- \frac{2}{x}$
The result is: $2 x - \frac{2}{x}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  2      
- - + 2*x
  x

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

-4 
---
  3
 x

$$- \frac{4}{x^{3}}$$

Simplify