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The derivative of the function/ 3x^5-8ln(x)

Derivative of 3x^5-8ln(x)

The solution

You have entered [src]

   5           
3*x  - 8*log(x)

$$3 x^{5} - 8 \log{\left(x \right)}$$

3*x^5 - 8*log(x)

Detail solution

Differentiate $3 x^{5} - 8 \log{\left(x \right)}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
  So, the result is: $15 x^{4}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  So, the result is: $- \frac{8}{x}$
The result is: $15 x^{4} - \frac{8}{x}$
Now simplify:

$\frac{15 x^{5} - 8}{x}$

The answer is:

$\frac{15 x^{5} - 8}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  8       4
- - + 15*x 
  x

$$15 x^{4} - \frac{8}{x}$$

Simplify

The second derivative [src]

  /2        3\
4*|-- + 15*x |
  | 2        |
  \x         /

$$4 \left(15 x^{3} + \frac{2}{x^{2}}\right)$$

Simplify

The third derivative [src]

  /  4        2\
4*|- -- + 45*x |
  |   3        |
  \  x         /

$$4 \left(45 x^{2} - \frac{4}{x^{3}}\right)$$

Simplify