 # Derivative of a logarithmic function tutor

Introduction:

In calculus, the derivative is a measure of how a function changes as its input changes. The process of finding a derivative is called differentiation. The derivative of logarithmic function is the derivatives of inverse of exponential function since the inverse of exponential function is logarithmic function.

Itis very easy for the students to learn derivative of logarithmic function from the tutor. The tutor explains every single topic with example problems, which can be easily understandable by the students.  A few example problems are given below to show how tutors help you for learning derivatives of logarithmic function.

(Source: Wikipedia)

## Learning derivative of a logarithmic function with example problems from the tutor:

Example 1:

Find the derivative of y = ln (8x)
Solution:

Step 1: Given function

y = ln (8x)

Using logarithmic identities, the given function can be written as

y = ln 8 + ln x

Step 2: Differentiate the function y = ln 8 + ln x with respect to ' x '

`(dy)/(dx)` = 0 + `1/x`

= `1/x`

Example 2:

Find the derivative of y = ln x6

Solution:

Step 1: Given function

y = ln x6

Using logarithmic identities, the given function can be written as

y = 6 log x

Step 2: Differentiate the function y = 6 log x with respect to ' x '

`(dy)/(dx)` = 6 `1/x`

= `6/x`

Example 3:

Find the derivative of y = ln (3x + 5)

Solution:

Step 1: Given function

y = ln (3x + 5)

Step 2: Differentiate the function y = ln (3x + 5) with respect to ' x '

`(dy)/(dx)` = `1/(3x + 5)` `d/(dx)` (3x + 5)

= `1/(3x + 5)` (3)

= `3/(3x + 5)`

## Learning derivative of a logarithmic function with practice problems from the tutor:

1) Find the derivative of the function y = 2ln (9x)

2) Find the derivative for the function y = 3ln x7

3) Find the derivative for the function y = ln (5x + 9)

Solutions:

1) `2/x`

2) `21/x`

3) `5/(5x + 9)`