Why is the derivative of the exponential function itself?

The exponential function is defined as a power series, which we may (for reasons that are beyond the scope of A-level) differentiate term by term to get another power series. The general term of the series differentiates to the term before it, the first term is 1 so disappears and the series is infinite which means the whole series differentiates to itself!

GB
Answered by George B. Maths tutor

3778 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How would I differentiate y = 3xy + 2x^2 + x^2y^2 ?


How to plot quadratic functions, e.g. F(x)= x^2 + 2x +1


Find ∫(8x^3 + 4) dx


Prove the identity (4cos(2x))/(1+cos(2x)) = 4-2sec^2(x)


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