MYTUTOR SUBJECT ANSWERS

608 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,...

1 year ago

Answered by Charlie, an A Level Maths tutor with MyTutor


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

371 SUBJECT SPECIALISTS

£26 /hr

Ellen T.

Degree: Economics (Bachelors) - LSE University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Economics
-Personal Statements-

“Hi! I study Economics at LSE. With previous tutoring experience, I am keen to provide genuine advice and create an engaging learning environment.”

£24 /hr

Hinsum W.

Degree: Medicine (Bachelors) - Edinburgh University

Subjects offered:Maths, Chemistry+ 3 more

Maths
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“I'm a 3rd year Edinburgh medic currently intercalating in Anaesthesia. I am a seasoned tutor and can improve your exam technique and subject knowledge!”

£30 /hr

Mathew V.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hi there! I’m Mathew, a 3rd year undergraduate student of Mathematics at Warwick University. For A-Levels I studied Maths, Further Maths, Further Additional Maths and Physics. I also worked at a local tuition centre for 2 years prior ...”

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

Does the equation: x^2+5x-6 have two real roots? If so what are they?

Is a line ax+by+c=0 tangent to a circle?

How to differentiate y=(x^2+4x)^5

y = 4x^3 - 5/x^2 Find dy/dx

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