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Math Help - Doubts about derivatives

  1. #1
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    Doubts about derivatives

    I started to learn calculus following a book but I donít understand the explanation of a derivative example. Here is the excerpt of the book:

    Then the Pythagorean theorem tells us that

    h(t)^2 + b(t)^2 = 13^2

    We may differentiate both sides of this equation with respect to the variable t
    (which is time in minutes) to obtain

    2 h(t) hí(t) + 2 b(t) bí(t) = 0

    It seems that the author applied the Chain Rule but I am not sure about the intermediary steps of this differentiation. Could someone show me the intermediary steps and explain them if needed ?
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  2. #2
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    Quote Originally Posted by tedhill View Post
    I started to learn calculus following a book but I donít understand the explanation of a derivative example. Here is the excerpt of the book:

    Then the Pythagorean theorem tells us that

    h(t)^2 + b(t)^2 = 13^2

    We may differentiate both sides of this equation with respect to the variable t
    (which is time in minutes) to obtain

    2 h(t) hí(t) + 2 b(t) bí(t) = 0

    It seems that the author applied the Chain Rule but I am not sure about the intermediary steps of this differentiation. Could someone show me the intermediary steps and explain them if needed ?
    We have,
    h^2(t)+b^2(t) = 13^2
    Now,
    h^2(t) can be thought of (mentally) as H(u) = u^2 \mbox{ where }u=h(t)
    So,
    \frac{d [ h^2(t)]}{dt} = \frac{dH}{du}\cdot \frac{du}{dx}=2u \cdot h'(t) = 2h'(t)h(t)

    Similary with b^2(t).
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  3. #3
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    Thank you, ThePerfectHacker.
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