Mister Exam

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The derivative of the function/ y=lnx+2x

Derivative of y=lnx+2x

The solution

You have entered [src]

log(x) + 2*x

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

log(x) + 2*x

Detail solution

Differentiate $2 x + \log{\left(x \right)}$ term by term:
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x$ goes to $1$
  So, the result is: $2$
The result is: $2 + \frac{1}{x}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    1
2 + -
    x

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

Simplify

The second derivative [src]

-1 
---
  2
 x

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

Simplify

The third derivative [src]

2 
--
 3
x

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

Simplify

The graph

Derivative of y=lnx+2x