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Math Help - Related Rates and logarithmic differentiation.

  1. #1
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    Related Rates and logarithmic differentiation.

    I was doing some homework and I've hit a roadblock on 3 questions. If you could help me out I would greatly appreciate it.

    I'm lost when it comes to logarithmic differentiation and 300 student lecture halls don't help either

    1. Water is leaking out of an inverted conical tank at a rate of 10,000 cm^3/min. At the same time, water is being pumped into the tank at a constant rate. The tank has a height of 6m and a diameter of 4m. If the water level is rising at a rate of 20cm/min when the height of the water is 2m. What is the rate that water is being pumped into the tank?

    2. Find and and simplify dy/dx for

    a. y=(1/x)^ln x
    b. y=ln(sqrt(x^2 + 4) - x)

    Once again thank you very much.
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  2. #2
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    Quote Originally Posted by GameTheory View Post
    I was doing some homework and I've hit a roadblock on 3 questions. If you could help me out I would greatly appreciate it.

    I'm lost when it comes to logarithmic differentiation and 300 student lecture halls don't help either

    1. Water is leaking out of an inverted conical tank at a rate of 10,000 cm^3/min. At the same time, water is being pumped into the tank at a constant rate. The tank has a height of 6m and a diameter of 4m. If the water level is rising at a rate of 20cm/min when the height of the water is 2m. What is the rate that water is being pumped into the tank?
    Well, what have you done on this? Can you at least set up the equations or draw a picture?

    2. Find and and simplify dy/dx for

    a. y=(1/x)^ln x
    ln(y)= ln((1/x)^ln x)= (ln x)(ln 1/x)= (ln x)(- ln x)= - (ln x)^2

    Can you differentiate both sides of that with respect to x?

    b. y=ln(sqrt(x^2 + 4) - x)
    This does NOT involve "logarithmic differentiation", just the chain rule.

    Once again thank you very much.
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