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The derivative of the function/ y=lnx+5lgx

Derivative of y=lnx+5lgx

The solution

You have entered [src]

log(x) + 5*log(x)

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

log(x) + 5*log(x)

Detail solution

Differentiate $\log{\left(x \right)} + 5 \log{\left(x \right)}$ 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. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  So, the result is: $\frac{5}{x}$
The result is: $\frac{6}{x}$

The answer is:

$\frac{6}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

6
-
x

$$\frac{6}{x}$$

Simplify

The second derivative [src]

-6 
---
  2
 x

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

Simplify

The third derivative [src]

12
--
 3
x

$$\frac{12}{x^{3}}$$

Simplify

The graph

Derivative of y=lnx+5lgx