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Homework Help: Year 11 Calculus Homework mainly focusing on Quotient Rule

  1. Oct 16, 2013 #1
    Hello. I am studying differential calculus and I need help on what these questions are asking and how to solve them. I have attempted some of the question but I need clarification. This week is mainly focused on learning the Quotient Rule. Please help me

    1. (a) Differentiate y = (x - A)/(x - B)
    (b) Show that for A>B, all tangents have a positive gradient, and for A<B all tangent have a negative gradient
    (c) What happens when A = B
    My attempt:
    (a) y' = (x-b)(1) - (x-A)(1) / (x - B)^2
    y' = (2x - AB) / (x - B)^2

    2. Evaluate f'(1) when
    (a) f(x) = (√x) + (√2) / (√x) - (√2)
    (b) f(x) = (2x-3)(√x + 1)/ x
    My attempt:
    (a) f'(x) = (√x-√2)(1/2√x)-(√x+√2)(1/2√x)/(√x -√2)^2
    = 1/2 - √2/2√x - 1/2 + √2/2√x
    = (-√2/√x)/ (√x-√2)^2
    f'(1) = (-√1) / (√1-√2)^2
    (-√1) = (√1-√2)^2
    I'm not sure what to do from here

    (b) f(x) = (2x-3)(√x + 1)/ x
    u = (2x-3)(√x + 1)
    v = x

    f'(x) =
    I don't know how to find the derivate to u. If I did I would only be able to get up to what I did in question 2. (a)

    With Q1 (b) and (c) am I supposed to equate the equation to A or B, like in quadratic equations? Or is that what I am supposed to do in Question 2. I am confused by what these questions are asking. Sorry if I haven't shown as much working out as I should have.

    Thank you for reading
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 17, 2013 #2


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    Science Advisor
    Homework Helper

    Why don't you just concentrate on 1(a) for a bit. Your simplification of the derivative is badly wrong. It's bad algebra. I don't even understand what you are doing. Then go on to the rest.
  4. Oct 17, 2013 #3
    Think of exactly what the quotient rule states. How would you then apply it to the expression y = (x-a)/(x-b) ?
  5. Oct 17, 2013 #4


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    Homework Helper

    Those square roots are wrong. Practice with the sum and product rules until you know them very well, then come back to the quotient rule. I say this because once you apply the quotient rule, you'll have sums and products to simplify.
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