Differentiate: y = 2 ^ x

y = 2 ^ x

take ln of both sides

ln( y) = ln (2 ^ x)

using the log rules we can bring the power of x down in front of the ln

ln( y ) = x*ln(2)

differentiate both sides wrt x

( 1 / y ) * dy / dx = ln(2)

dy / dx = y*ln(2)   ==> rememer  y = 2 ^ x

dy / dx = ln(2) * 2 ^ x

Answered by Shantu H. Maths tutor

52170 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate sin(x)cos(x)^2 from 0 to π/2


Give the first and second derivative of the function f(x) = 5/x - 9x + 4


Outline the various ways that you can differentiate a function


How do I remember the trigonometry identities from C3 in the exam?


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