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Rates of Change/Integration - help needed

  1. Oct 12, 2011 #1
    1. The problem statement, all variables and given/known data

    Due to illness, I missed my calculus class and can't do the homework my friend gave me.

    Q1) The volume of a sphere is increasing at a rate of 75cm^3s^-1. Find the rate at which the radius is increasing at the instant when the radius of the sphere is 15cm.

    Q2) Find the gradient of the curve y=5e^3x at the point for which x=ln a, giving your answer in simplified form in terms of the constant a.

    2. Relevant equations

    3. The attempt at a solution
    Q1) First idea was to use the chain rule?

    Q2) y=5e^3x, dy/dx=15e^3x. Substitute x=ln a and rearrange to find a?
    Last edited by a moderator: Oct 12, 2011
  2. jcsd
  3. Oct 12, 2011 #2


    Staff: Mentor

    No, the first thing to do is to establish a relationship between the volume V and the radius r.
    Then find a relationship between the rates (i.e., derivatives with respect to time) of those variables.
    Use parentheses around the exponents.

    Let y = f(x) = 5e^(3x). Then f'(x) = 15e^(3x).
    f'(lna) = ?
    They are not asking you to find a.
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