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Derivative of:
Derivative of (x+x^2)^x
Derivative of -sin(x)+cos(x)
Derivative of sin(x)-2*x
Derivative of f(x)=1/3x²+x²+2x
Identical expressions
xlnx+(x^ two)/ four
xlnx plus (x squared ) divide by 4
xlnx plus (x to the power of two) divide by four
xlnx+(x2)/4
xlnx+x2/4
xlnx+(x²)/4
xlnx+(x to the power of 2)/4
xlnx+x^2/4
xlnx+(x^2) divide by 4
Similar expressions
xlnx-(x^2)/4

The derivative of the function/ xlnx+(x^2)/4

Derivative of xlnx+(x^2)/4

The solution

You have entered [src]

            2
           x 
x*log(x) + --
           4

$$\frac{x^{2}}{4} + x \log{\left(x \right)}$$

x*log(x) + x^2/4

Detail solution

Differentiate $\frac{x^{2}}{4} + x \log{\left(x \right)}$ term by term:
1. Apply the product rule:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Apply the power rule: $x$ goes to $1$
  $g{\left(x \right)} = \log{\left(x \right)}$ ; 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: $\log{\left(x \right)} + 1$
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: $\frac{x}{2}$
The result is: $\frac{x}{2} + \log{\left(x \right)} + 1$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    x         
1 + - + log(x)
    2

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

Simplify

The second derivative [src]

1   1
- + -
2   x

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

Simplify

The third derivative [src]

-1 
---
  2
 x

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

Simplify