What is the derivative of ln(x)?

First let y=ln(x).

Recall that the exponential function, ex, is defined as the inverse of the logarithmic function, ln(x).

To make x the subject of the formula, use the inverse function exp. This gives that x=ey.

Now, differentiate both sides with respect to y and recall that d/dx(ex)=ex. This gives dx/dy=ey.

Remember for a derivative, dy/dx=1/(dx/dy).

Therefore, dy/dx=1/ey.

Finally, from above, x=ey.

Substituting for ey we have dy/dx=1/x which is our final result.

Therefore the derivative of ln(x), is dy/dx=1/x.

Answered by Benjamin G. Maths tutor

6471 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

y = x^x, find y'


What is the turning point on the curve f(x) = 2x^2 - 2x + 4


Given that (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2) = 7, show that tan(x)^2 = 3/2


A curve, C, has equation y =(2x-3)^5. A point, P, lies on C at (w,-32). Find the value of w and the equation of the tangent of C at point, P in the form y =mx+c.


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