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

149707 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can we calculate the derivative of function f(x)= (x+2)/(x-1)?


(5 + 2(2^0.5))(7 - 3(2^0.5))


Simplify and solve for x. log(x+1)+log 5=2. Note, log is the natural log in this case


Differentiate ln(x)/x


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences