Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (x+3)^4
Derivative of (x^2-x)*(x^3+x)
Derivative of (x-2)^4
Derivative of (x^2-1)*(x^4+2)
Integral of d{x}:
x^3*ln(x)
Graphing y =:
x^3*ln(x)
Identical expressions
x^ three *ln(x)
x cubed multiply by ln(x)
x to the power of three multiply by ln(x)
x3*ln(x)
x3*lnx
x³*ln(x)
x to the power of 3*ln(x)
x^3ln(x)
x3ln(x)
x3lnx
x^3lnx
Similar expressions
x^3ln(x)

The derivative of the function/ x^3*ln(x)

Derivative of x^3*ln(x)

The solution

You have entered [src]

 3       
x *log(x)

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

d / 3       \
--\x *log(x)/
dx

$$\frac{d}{d x} x^{3} \log{\left(x \right)}$$

Transform

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{3}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
$g{\left(x \right)} = \log{\left(x \right)}$ ; 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: $3 x^{2} \log{\left(x \right)} + x^{2}$
Now simplify:

$x^{2} \cdot \left(3 \log{\left(x \right)} + 1\right)$

The answer is:

$x^{2} \cdot \left(3 \log{\left(x \right)} + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

x*(5 + 6*log(x))

$$x \left(6 \log{\left(x \right)} + 5\right)$$

Simplify

The third derivative [src]

11 + 6*log(x)

$$6 \log{\left(x \right)} + 11$$

Simplify

The graph

Derivative of x^3*ln(x)