Hey there! Sign in to join this conversationNew here? Join for free

Differentiation help please... Watch

Announcements
    • Thread Starter
    Offline

    0
    ReputationRep:
    A curve has equation y= e^{-4x}(x^{2}+2x-2)
    Show that \frac{dy}{dx} = 2e^{-4x}(5-3x-2x^{2})

    How do you do this? I differentiated the e^{-4x} and got -4ex^{-4x} and the differentiated the bracket bit to get (2x+2) :/
    Offline

    15
    ReputationRep:
    (Original post by Nkhan)

    A curve has equation: e^{-4x}(x^{2}+2x-2)
    Show that \frac{dy}{dx} = 2e^{-4x}(5-3x-2x^{2})

    Well have you tried using the product rule?

    (u x dv/dx) + (v x du/dx)

    where u = the first part of your function and v = the second part of the function
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Mr_Muffin_Man)
    Well have you tried using the product rule?

    (u x dv/dx) + (v x du/dx)

    where u = the first part of your function and v = the second part of the function
    I differentiated the e^{-4x} and got -4ex^{-4x} and the differentiated the bracket bit to get (2x+2) :/
    Offline

    3
    ReputationRep:
    (Original post by Nkhan)
    I differentiated the e^{-4x} and got -4ex^{-4x} and the differentiated the bracket bit to get (2x+2) :/
    Your function is product of an exponential and a polinomial function,
    let u=f(x) and v=g(x) so y=f(x)*g(x)
    Derivating y (dy/dx)you should use the product rule for these type of functions.
    This rule: Y' =f'(x)*g(x) + f(x)*g'(x)
    Offline

    3
    ReputationRep:
    As others have said, product rule that shizzle.
    Offline

    0
    ReputationRep:
    Seriously? Apply the Product Rule!!!
    Offline

    0
    ReputationRep:
    



y\ =\ (e^-4x )(x^2 +2x-2)



u= e^-4x

\dfrac{du}{dx}\ = -4e^-4x



v= x^2 +2x-2

\dfrac{dv}{dx}\ = 2x+2



Product Rule = u dv/dx + v du/dx



= (e^-4x)(2x+2) - 4e^-4x (x^2 +2x-2)



= 2(e^-4x)(x+1) - 4e^-4x (x^2 +2x-2)



= 2(e^-4x)(x+1) - 2(e^-4x) 2(x^2 +2x-2)



= 2e^-4x ((x+1) - 2(x^2 +2x-2))



= 2e^-4x (5-3x-2x^2 )

    Hope that helps!q
    Offline

    0
    ReputationRep:
    See more solved problems on product rule at http://www.math24.net/derivative-of-...-quotient.html.
    Offline

    0
    ReputationRep:
    (Original post by Nkhan)
    A curve has equation y= e^{-4x}(x^{2}+2x-2)
    Show that \frac{dy}{dx} = 2e^{-4x}(5-3x-2x^{2})

    How do you do this? I differentiated the e^{-4x} and got -4ex^{-4x} and the differentiated the bracket bit to get (2x+2) :/
    product rule: dy/dx of uv = v(du/dx) + u(dv/dx)

    uv = [e^(-4x)] (x^2+2x-2)

    therefore u = [e^(-4x)] and v = (x^2 + 2x - 2)
    du/dx = -4e^(-4x) and dv/dx = 2x + 2

    using that formula:

    (x^2 + 2x - 2)[-4e^(-4x)] + [e^(-4x)](2x+2)

    simplifying will hopefully give you the 'show that' answer
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Will you be richer or poorer than your parents?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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