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.

Answered by James C. Maths tutor

7497 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve has equation y = f(x) and passes through the point (4, 22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7, use integration to find f(x), giving each term in its simplest form


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


Differentiate with respect to x: 4(x^3) + 2x


Integrate x^2e^x with respect to x between the limits of x=5 and x=0.


We're here to help

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