Derivative of y=lnx+x^3

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          3
log(x) + x

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

log(x) + x^3

Detail solution

Differentiate $x^{3} + \log{\left(x \right)}$ term by term:
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
2. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
The result is: $3 x^{2} + \frac{1}{x}$
Now simplify:

$\frac{3 x^{3} + 1}{x}$

The answer is:

$\frac{3 x^{3} + 1}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1      2
- + 3*x 
x

$$3 x^{2} + \frac{1}{x}$$

Simplify

The second derivative [src]

$$6 x - \frac{1}{x^{2}}$$

Simplify

3-я производная [src]

  /    1 \
2*|3 + --|
  |     3|
  \    x /

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

Simplify

The third derivative [src]

  /    1 \
2*|3 + --|
  |     3|
  \    x /

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

Simplify

The graph