Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Find the gradient of the curve y=5e^3x at the point for which x= (ln a)




    Could someone please explain why the answer is 15a^3 ????
    Offline

    17
    ReputationRep:
    What do you get when you differentiate that? Once you get dy/dx, that's you gradient formula, you just plug in the x value and you will get 15a^3
    Offline

    2
    ReputationRep:
    (Original post by FoOtYdUdE)
    Find the gradient of the curve y=5e^3x at the point for which x= (ln a)




    Could someone please explain why the answer is 15a^3 ????
    What did you get when you differentiated it?
    Edit: too slooooooooow
    Offline

    14
    ReputationRep:
    The differential wrt x is 15e^3x.

    This gives the rate of change of y wrt x, i.e. the gradient, at some x.

    At x=lna, 3x=3lna=ln(a^3)

    Thus the gradient is 15*e^[ln(a^3)]=15a^3
    Offline

    0
    ReputationRep:
    remember that e^kx differentiated is ke^kx
    Offline

    0
    ReputationRep:
    15e^3x, then put sub x with lna
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Mr.Singh)
    15e^3x, then put sub x with lna
    yeah, i get the 15e^3x part....but u know when you subsititue it...i don't see why the 3 remains as a power and the a comes down. :confused:
    Offline

    2
    ReputationRep:
    (Original post by FoOtYdUdE)
    yeah, i get the 15e^3x part....but u know when you subsititue it...i don't see why the 3 remains as a power and the a comes down. :confused:
    k ln x = ln(x^k)
    Can you do it from there?
    • Thread Starter
    Offline

    0
    ReputationRep:
    ok, so 15e^(3 x ln a)

    i get stuck after writing that.
    Offline

    0
    ReputationRep:
    when u have the power=3lna
    the 3 goes to the front as a power of a. the e and ln are like them inversey thingies so they cancle leaving 15a^3 cos the 3 is still the power of a
    Offline

    17
    ReputationRep:
    (Original post by FoOtYdUdE)
    ok, so 15e^(3 x ln a)

    i get stuck after writing that.
     3 lna = ln a^ 3

     e^{ln Q} = Q
    • Thread Starter
    Offline

    0
    ReputationRep:
    OMG guys, i love you!!!!!!! Thank you. Sorry for being so dumb. :o:
    Offline

    0
    ReputationRep:
    footy dude. look at the rules of e and ln on this website. its good for revision http://www.mathsrevision.net/alevel/pure/
    Offline

    17
    ReputationRep:
    (Original post by Naffy)
    you guys are making it too confusing.

    e and ln cancel out, thats all there is too it (ignore the above) no offense to 2710, but you're overcomplicated a 'relatively' simple C3 question
    What are you talking about? In my post I showed that e and ln cancel out. I dont think theres anything hard about it...
    Offline

    0
    ReputationRep:
    (Original post by Naffy)
    you guys are making it too confusing.

    e and ln cancel out, thats all there is too it (ignore the above) no offense to 2710, but you're all overcomplicating a 'relatively' simple C3 question

    ln a x e = a
    i think you'll find that's not true.

    For example:

    ln(3) * e = 2.98633782
    ln(6) * e = 4.87050721

    However, e^{ln\ a} = a

    e^{ln\ 3} = 3
    e^{ln\ 6} = 6
    Offline

    14
    ReputationRep:
    y=5e^3x
    dy/dx=15e^3x
    when x=ln(a)
    dy/dx=15e^3ln(a)--->e^ln cancel each other out so that a goes down
    so you get: dy/dx=15a^3
    Offline

    11
    ReputationRep:
    (Original post by zdo0o)
    i think you'll find that's not true.
    I noticed my mistake, thats why I deleted straight after. I misunderstood that you guys were trying to explain the change of power log law.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 16, 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.