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Derivative of:
Derivative of 7*x
Derivative of log(5)
Derivative of asin(sqrt(x))
Derivative of x^-(1/2)
Identical expressions
x^ seven *log(x)
x to the power of 7 multiply by logarithm of (x)
x to the power of seven multiply by logarithm of (x)
x7*log(x)
x7*logx
x⁷*log(x)
x^7log(x)
x7log(x)
x7logx
x^7logx

The derivative of the function/ x^7*log(x)

Derivative of x^7*log(x)

The solution

You have entered [src]

 7       
x *log(x)

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

x^7*log(x)

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{7}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{7}$ goes to $7 x^{6}$
$g{\left(x \right)} = \log{\left(x \right)}$ ; 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: $7 x^{6} \log{\left(x \right)} + x^{6}$
Now simplify:

$x^{6} \left(7 \log{\left(x \right)} + 1\right)$

The answer is:

$x^{6} \left(7 \log{\left(x \right)} + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 6      6       
x  + 7*x *log(x)

$$7 x^{6} \log{\left(x \right)} + x^{6}$$

Simplify

The second derivative [src]

 5                 
x *(13 + 42*log(x))

$$x^{5} \left(42 \log{\left(x \right)} + 13\right)$$

Simplify

The third derivative [src]

 4                   
x *(107 + 210*log(x))

$$x^{4} \left(210 \log{\left(x \right)} + 107\right)$$

Simplify