Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hi All

    Please help a returning mature student...
    Help needed with 2 Differentiation Questions.

    Q= 2e^x + e^-2x
    A= 2e^x + -2e^-2x

    Why would they keep 2e^x in the answer ?
    I do understand the -2e^-2x part though managed to work that one out correctly..

    Q= sin(-8Q) the Q is supposed to be theta dont know how to write it on keyboard.
    A= I would tend to give -8 Cos -8Q but the actual answer is
    -8Cos(-8Q)=-8Cos 8Q. So I dont understand how they come to that please help.

    Kind regards
    SZia
    Offline

    15
    ReputationRep:
    When writing down answers, it's best not to use Q=... and A=... as this is not a standard notation so it can be confusing. Instead, you can use the notation \frac{d}{dx}f(x)=g(x) which means that if you differentiate f(x) you get g(x). So for example, you might write your answer to the first question as \dfrac{d}{dx}(2e^x+e^{-2x})=2e^x-2e^{-2x}.

    Anyway, to answer your question, when you differentiate 2e^x you can use the chain rule if you're not sure. So let y=2e^x and u=e^x so y=2u. Now \dfrac{dy}{dx} = \dfrac{dy}{du} \times \dfrac{du}{dx}= 2 \times  e^x = 2e^x. So if we differentiate 2e^x we get 2e^x.

    For the second part, sketch a graph of y=cos(x). You'll notice that the graph is symmetrical about the y axis, so we could swap round the x and -x axes and still get the same graph. What this means mathematically is that cos(x)=cos(-x) which is a general trigonometric identity that is useful to know. So in your case, you have -8\cos(-8\theta) so using this identity we have, we can say that this is equal to -8\cos(8\theta). What this does is it eliminates an extra minus sign, making the answer slightly simpler.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: September 24, 2010

University open days

  1. University of Bradford
    University-wide Postgraduate
    Wed, 25 Jul '18
  2. University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Wed, 25 Jul '18
  3. Bournemouth University
    Clearing Campus Visit Undergraduate
    Wed, 1 Aug '18
Poll
How are you feeling in the run-up to Results Day 2018?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.