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Math Help - Derivative

  1. #1
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    Derivative

    differentiate ))

    Hey I must say this is an awesome site!!

    q1.) y = tanh ^ -1 (3x^5)

    using chain rule.

    u=3x^5 du/dx = 15x^4

    y= tanh ^ -1 (u) dy/du = 1/1-u^2 . (u) >>> SO; 1/(1-3x^5)^2 . (u)

    y' = (3x^5 / 1 - 9x^10) . (15x^4)

    or should it just be

    y' = 15x^4 / 1-9x^10
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  2. #2
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    Quote Originally Posted by Jon123 View Post
    differentiate ))

    Hey I must say this is an awesome site!!

    q1.) y = tanh ^ -1 (3x^5)

    using chain rule.

    u=3x^5 du/dx = 15x^4

    y= tanh ^ -1 (u) dy/du = 1/1-u^2 . (u) >>> SO; 1/(1-3x^5)^2 . (u)

    y' = (3x^5 / 1 - 9x^10) . (15x^4)

    or should it just be

    y' = 15x^4 / 1-9x^10
    The second answer is correct. I'm not sure why you are including the 3x^5 in the numerator of the first.

    -Dan

    Edit: Oh your second answer was correct, but a little matter of typing. This line has problems:
    dy/du = 1/1-u^2 . (u) >>> SO; 1/(1-3x^5)^2 . (u)

    First dy/du = 1/(1 - u^2) (watch the parenthesis!), so upon subbing in u = 3x^5 you get dy/dx = 1/(1 - (3x^5)^2) * du/dx. Note the form of the denominator. Also note that it is du/dx that shows up here, not u. The full chain rule is
    \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}
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