How do you differentiate 2 to the power x?

let y=2x                 {take natural logs of both sides}

ln y = ln(2x)          {use rules of logs to change right hand side}

lny = xln2              {differentiate implicitly}

1/y dy/dx = ln2    {make dy/dx the subject}

dy/ dx       = y ln2  {write y in terms of x)

dy/dx = 2x . ln2

Therefore derivative of 2 to the power of x is 2x . ln2

 

This can be generalised as the derivative of a to the power of x (where a is a constant, a>0)  is  ax lna

JR
Answered by Jack R. Maths tutor

146136 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can I try and solve this differentiation, I don`t understand it?


Prove the identity (sin2x)/(1+(tanx)^2) = 2sinx(cosx)^3


The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the


A curve C has the equation x^3 + 6xy + y^2 = 0. Find dy/dx in terms of x and y.


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