How do I prove that the differential of coshx is equal to sinhx?

Before this proof, it is important to appreciate that both of these hyperbolic  functions can be written in terms of e^x. Therefore, before you begin to differentiate, you must represent coshx as (e^x + e^-x)/2. Then, this can easily be differentiated to give you the answer (e^x-e^-x)/2, which is the equivalent of sinhx.

TR
Answered by Thomasina R. Further Mathematics tutor

2813 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

What are imaginary numbers, and why do we bother thinking about them if they don't exist?


The complex number -2sqrt(2) + 2sqrt(6)I can be expressed in the form r*exp(iTheta), where r>0 and -pi < theta <= pi. By using the form r*exp(iTheta) solve the equation z^5 = -2sqrt(2) + 2sqrt(6)i.


Find the complementary function to the second order differential equation d^2y/dx^2 - 5dy/dx + 6x = x^2


Prove e^(ix) = cos (x) + isin(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