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

13502 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Show that x^2 - 8x +17 <0 for all real values of x


Find the stationary points of the function f(x) = x^3 - 27x and determine whether they are maxima or minima


Integrate 2x^3 -4x +5


y = arcsec(x), Find dy/dx.


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