Mister Exam

Other calculators

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

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

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
              2    
2*x*log(x) - x  + 3
(−x2+2xlog⁡(x))+3\left(- x^{2} + 2 x \log{\left(x \right)}\right) + 3 
(2*x)*log(x) - x^2 + 3
Detail solution

  1. Differentiate (−x2+2xlog⁡(x))+3\left(- x^{2} + 2 x \log{\left(x \right)}\right) + 3 term by term:

    1. Differentiate −x2+2xlog⁡(x)- x^{2} + 2 x \log{\left(x \right)} term by term:

      1. Apply the product rule:

        ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\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(x)=2xf{\left(x \right)} = 2 x; to find ddxf(x)\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: xx goes to 11

          So, the result is: 22

        g(x)=log⁡(x)g{\left(x \right)} = \log{\left(x \right)}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

        1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

        The result is: 2log⁡(x)+22 \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: x2x^{2} goes to 2x2 x

        So, the result is: −2x- 2 x

      The result is: −2x+2log⁡(x)+2- 2 x + 2 \log{\left(x \right)} + 2

    2. The derivative of the constant 33 is zero.

    The result is: −2x+2log⁡(x)+2- 2 x + 2 \log{\left(x \right)} + 2

The answer is:

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

The graph
02468-8-6-4-2-1010-10050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
2 - 2*x + 2*log(x)
−2x+2log⁡(x)+2- 2 x + 2 \log{\left(x \right)} + 2
Simplify
The second derivative [src] 
  /     1\
2*|-1 + -|
  \     x/
2(−1+1x)2 \left(-1 + \frac{1}{x}\right)
Simplify
The third derivative [src] 
-2 
---
  2
 x
−2x2- \frac{2}{x^{2}}
Simplify
    © Mister Exam – Calculator