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Derivative of:
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Identical expressions
two x(lnx)-x^2+ three
2x(lnx) minus x squared plus 3
two x(lnx) minus x squared plus three
2x(lnx)-x2+3
2xlnx-x2+3
2x(lnx)-x²+3
2x(lnx)-x to the power of 2+3
2xlnx-x^2+3
Similar expressions
2x(lnx)+x^2+3
2x(lnx)-x^2-3

The derivative of the function/ 2x(lnx)-x^2+3

Derivative of 2x(lnx)-x^2+3

The solution

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              2    
2*x*log(x) - x  + 3

$$\left(- x^{2} + 2 x \log{\left(x \right)}\right) + 3$$

(2*x)*log(x) - x^2 + 3

Detail solution

Differentiate $\left(- x^{2} + 2 x \log{\left(x \right)}\right) + 3$ term by term:
1. Differentiate $- x^{2} + 2 x \log{\left(x \right)}$ term by term:
  1. Apply the product rule:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = 2 x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $2$
    $g{\left(x \right)} = \log{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
    1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
    The result is: $2 \log{\left(x \right)} + 2$
  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: $- 2 x$
  The result is: $- 2 x + 2 \log{\left(x \right)} + 2$
2. The derivative of the constant $3$ is zero.
The result is: $- 2 x + 2 \log{\left(x \right)} + 2$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2 - 2*x + 2*log(x)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

-2 
---
  2
 x

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

Simplify