Find the derivative of ln &#x2061;<!-- ⁡ --> ( x ) </mrow

hafusxl

hafusxl

Answered question

2022-05-01

Find the derivative of ln ( x ) e x .

Answer & Explanation

Kathleen Keller

Kathleen Keller

Beginner2022-05-02Added 20 answers

Differentiate using the Quotient Rule which states that d d x [ f ( x ) g ( x ) ] is g ( x ) d d x [ f ( x ) ] f ( x ) d d x [ g ( x ) ] g ( x ) 2
where f ( x ) = ln ( x ) and g ( x ) = e x
e x d d x [ ln ( x ) ] ln ( x ) d d x [ e x ] ( e x ) 2
The derivative of ln ( x ) with respect to x is 1 x
e x 1 x ln ( x ) d d x [ e x ] ( e x ) 2
Differentiate using the Exponential Rule which states that d d x [ a x ] is a x ln ( a ) where a=e.
e x 1 x ln ( x ) e x ( e x ) 2
Simplify.
e x ( x ln ( x ) 1 ) x

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?