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Derivative of:
Derivative of arctg(1/x)
Derivative of e^cos(x)
Derivative of ln(x+3)^3
Derivative of cot(1/x)
Integral of d{x}:
x^2*ln(x)
Graphing y =:
x^2*ln(x)
Identical expressions
x^ two *ln(x)
x squared multiply by ln(x)
x to the power of two multiply by ln(x)
x2*ln(x)
x2*lnx
x²*ln(x)
x to the power of 2*ln(x)
x^2ln(x)
x2ln(x)
x2lnx
x^2lnx
Similar expressions
x^2*lnx+e^2x
x^2(ln(x+sinx))(x+sinx)^x^2

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

Derivative of x^2*ln(x)

The solution

You have entered [src]

 2       
x *log(x)

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

x^2*log(x)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
$g{\left(x \right)} = \log{\left(x \right)}$ ; 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: $2 x \log{\left(x \right)} + x$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

x + 2*x*log(x)

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

Simplify

The second derivative [src]

3 + 2*log(x)

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

Simplify

The third derivative [src]

2
-
x

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

Simplify

The graph

Derivative of x^2*ln(x)