MYTUTOR SUBJECT ANSWERS

332 views

Why does ln(x) differentiate to 1/x ?

At first glance, this may seem quite complicated. However, it is simple once you make use of exponents. 

Let y=ln(x)

This can be written as: e= eln(x)

e to the power of a natural log cancels out, which gives: 

ey=x

Differentiating both sides with respect to x gives:

ey (dy/dx)=1 

[This uses implicit differentiation.  Remember that you must multiply ey by dy/dx as there isn't an x on that side]

Substituting in ey=x gives:

x (dy/dx) =1

And so dy/dx = 1/x

Charlie E. GCSE Physics tutor, GCSE Maths tutor, A Level Maths tutor,...

8 months ago

Answered by Charlie, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

297 SUBJECT SPECIALISTS

William S. 11 Plus Maths tutor, A Level Maths tutor, 13 plus  Maths t...
£20 /hr

William S.

Degree: Medicine (Other) - St. Andrews University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
Chemistry

“I am a medical student at the university of St Andrews. I have always loved maths and sciences, and hope to share that passion with you too! I am patient and very friendly, so hopefully you will enjoy our sessions. Of course, you will...”

£20 /hr

Matt M.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hi! My name's Matt and I'm a first year Maths student at the University of Bristol. I love Maths, especially when I can help other people to understand it.”

MyTutor guarantee

£20 /hr

Elena S.

Degree: Mechanical Engineering MEng (Masters) - Imperial College London University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Further Mathematics
Chemistry
Biology

“I am currently studying Mechanical Engineering at Imperial College London. This comes out of my passion for forming real life solutions to problems and love of problem solving. It’s this that inspires my tutoring also. Throughout univ...”

About the author

£20 /hr

Charlie E.

Degree: Physics (Masters) - Warwick University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Chemistry

“About Me Hi. I’m Charlie and I’m a physics student at Warwick University. I really enjoy physics and maths, and hope that I can share my passion with you. In my spare time, I play football and squash.  I’m verypatient, and we will go ...”

MyTutor guarantee

You may also like...

Posts by Charlie

Differentiate ln(x)/x

Why does ln(x) differentiate to 1/x ?

Other A Level Maths questions

Prove why the quadratic formula works

What is the equation of the curve that has gradient dy/dx=(4x-5) and passes through the point (3,7)?

If x = cot(y) what is dy/dx?

A curve is defined by the parametric equations x=t^2/2 +1, y=4/t -1. Find the gradient of the curve when t =2.

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok