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Derivative of:
Derivative of x^12
Derivative of e^-1
Derivative of sin^3*x
Derivative of sen2x
Limit of the function:
x^4*log(x)
Integral of d{x}:
x^4*log(x)
Identical expressions
x^ four *log(x)
x to the power of 4 multiply by logarithm of (x)
x to the power of four multiply by logarithm of (x)
x4*log(x)
x4*logx
x⁴*log(x)
x^4log(x)
x4log(x)
x4logx
x^4logx

The derivative of the function/ x^4*log(x)

Derivative of x^4*log(x)

The solution

You have entered [src]

 4       
x *log(x)

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

x^4*log(x)

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{4}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
$g{\left(x \right)} = \log{\left(x \right)}$ ; 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: $4 x^{3} \log{\left(x \right)} + x^{3}$
Now simplify:

$x^{3} \left(4 \log{\left(x \right)} + 1\right)$

The answer is:

$x^{3} \left(4 \log{\left(x \right)} + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 3      3       
x  + 4*x *log(x)

$$4 x^{3} \log{\left(x \right)} + x^{3}$$

Simplify

The second derivative [src]

 2                
x *(7 + 12*log(x))

$$x^{2} \left(12 \log{\left(x \right)} + 7\right)$$

Simplify

The third derivative [src]

2*x*(13 + 12*log(x))

$$2 x \left(12 \log{\left(x \right)} + 13\right)$$

Simplify

The graph

Derivative of x^4*log(x)