How do you differentiate 2^x?

We can differentiate this implicitly by writing the question as:y = 2Then we take the log of both sides:ln(y) = ln(2x)Using the rules of logartithms this can be written as:ln(y) = x ln(2)Now we can differentiate this easily:y-1 dy/dx = ln(2)We can now re-arrange to get:dy/dx = y ln(2)And finally we can substitute y to get our answer:dy/dx = 2ln(2)So we have shown that the derrivative of 2x is simply 2x multiplied by ln(2)

AC
Answered by Alex C. Maths tutor

13407 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Given that x = 4sin(2y + 6), Find dy/dx in terms of x


Differentiate (2^x)(5x^2+5x)^2.


How do you prove a mathematical statement via contradiction?


Find dy/dx when y = 4x^1/2


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning