Show that the derivative of ln(x) = 1/x

We can start by letting y = ln(x)

What we are trying to show is that dy/dx = 1/x

Since y = ln(x), then e= eln(x) = x

Taking the derivative of each side of this equation will give us ey.dy/dx = 1

If we divide each side of this new equation by ethen we have that dy/dx = 1/ey = 1/x as required.

JC
Answered by James C. Maths tutor

8296 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate with respect to x ) dy/dx= 6x^5


Solve the inequality x^2 > 3(x + 6)


Find the tangent for the line y=x^3+3x^2+4x+2 at x=2


How do I know if I am using the right particular integral when solving a differential equation


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences