Mister Exam

Lang:

The derivative of the function/ x*ln(x)

Derivative of x*ln(x)

The solution

You have entered [src]

x*log(x)

$$x \log{\left(x \right)}$$

x*log(x)

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1 + log(x)

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

Simplify

The second derivative [src]

1
-
x

$$\frac{1}{x}$$

Simplify

The third derivative [src]

-1 
---
  2
 x

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

Simplify

The graph

Derivative of x*ln(x)