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Math Help - Derivation of n functions

  1. #1
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    Derivation of n functions

    Calculate

    1) z=e^\frac{s}{t}, s=xy^2 and t=5x+2y^3. Calculate \frac{dz}{dx} and \frac{dz}{dy}

    My solution:

    \frac{dz}{dx} = \frac{dz}{ds} \frac{ds}{dx} + \frac{dz}{dt} \frac{dt}{dx}

    \frac{dz}{dx}= \frac{y^2e^\frac{s}{t}}{t}-\frac{5se^\frac{s}{t}}{t^2}

    The answer is correct?

    \frac{dz}{dy} = \frac{2xye^\frac{s}{t}}{t}-\frac{6yse^\frac{s}{t}}{t^2} ????
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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    Calculate

    1) z=e^\frac{s}{t}, s=xy^2 and t=5x+2y^3. Calculate \frac{dz}{dx} and \frac{dz}{dy}

    My solution:

    \frac{dz}{dx} = \frac{dz}{ds} \frac{ds}{dx} + \frac{dz}{dt} \frac{dt}{dx}

    \frac{dz}{dx}= \frac{y^2e^\frac{s}{t}}{t}-\frac{5se^\frac{s}{t}}{t^2}

    The answer is correct? Yes.

    \frac{dz}{dy} = \frac{2xye^\frac{s}{t}}{t}-\frac{6yse^\frac{s}{t}}{t^2} ???? y should be y^2 in the second fraction. Otherwise it's correct.
    And of course all the d's should be partial d's (\partial in LaTeX).
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  3. #3
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    thank you
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