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30 May, 07:03

Find the dy/dx xy = (x+y) ^4

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  1. 30 May, 10:11
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    dy/dx = (4 (x + y) ^3 - y) / (x - 4 (x + y) ^3).

    Step-by-step explanation:

    xy = (x + y) ^4

    Using implicit differentiation:

    x dy/dx + y*1 = 4 (x + y) ^3 * (1 + dy/dx)

    x dy/dx + y = 4 (x + y) ^3 + 4 dy/dx (x + y) ^3

    x dy/dx - 4 dy/dx (x + y) ^3 = 4 (x + y) ^3 - y

    dy/dx (x - 4 (x + y) ^3) = 4 (x + y) ^3 - y

    dy/dx = (4 (x + y) ^3 - y) / (x - 4 (x + y) ^3)
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