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: 


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,...

6 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


£20 /hr

Oliver T.

Degree: Mathematics (Masters) - Edinburgh University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“Hello! I'm currently a 2nd year Mathematics student at the University of Edinburgh with a sturdy passion for all things Mathematics. Not only do I love Maths, I love teaching Maths and helping people with problems. In particular, I en...”

MyTutor guarantee

£22 /hr

Cordelia W.

Degree: Mathematical Science (Masters) - Durham University

Subjects offered: Maths, Physics+ 1 more

Further Mathematics

“I LOVE maths and believe I can pass on my love of the subject. I have been teaching maths and physics for years. I taught myself maths and physics, I helped my friends understand both subjects, I went on toteach a whole secondary scho...”

£20 /hr

Charlotte G.

Degree: Medicine (Bachelors) - University College London University

Subjects offered: Maths, Chemistry+ 2 more

.BMAT (BioMedical Admissions)

“About Me: I am a medical student at University College London (UCL) who has always had a real passion for science and finding out how things work. I adore Medicine, I very much enjoyed learning about biology, maths and chemistry at s...”

About the author

£20 /hr

Charlie E.

Degree: Physics (Masters) - Warwick University

Subjects offered: Maths, Physics+ 1 more


“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

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

Where does the geometric series formula come from?

A girl saves money over 200 weeks. She saves 5p in Week 1, 7p in Week 2, 9p in Week 3, and so on until Week 200. Her weekly savings form an arithmetic sequence. Find the amount she saves in Week 200. Calculate total savings over the 200 week period.

How do you differentiate X to the power of a?

View A Level Maths tutors


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