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4 June, 08:33

Given y = f (u) and u = g (x), find dy/dx = f' (g (x)) g' (x).

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  1. 4 June, 11:13
    0
    Due to the sensitivity of writing f (u), it's derivatives, and other terms that contain it, I replaced f (u) by h (u).

    Step-by-step explanation:

    Answer:

    dy/dx = (dy/dw) * (dw/dx)

    = h' (g (x)) g' (x)

    Step-by-step explanation:

    Given y = h (w), and w = g (x)

    dy/dx can be obtained by applying Chain Rule by finding dy/du and du/dx, and multiplying them. That is,

    dy/dx = (dy/du) * (du/dx)

    y = h (u)

    dy/du = h' (u)

    u = g (x)

    dw/dx = g' (x)

    Since w = g (x), we can write h' (u) as h' (g (x)).

    So,

    dy/du = h' (g (x))

    dy/dx = (dy/du) * (du/dx)

    = h' (g (x)) * g' (x)

    = h' (g (x)) g' (x)

    Which is exactly what we are trying to obtained if we replaced "h" by "f".
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