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Dorian Vaughan
Mathematics
1 October, 01:48
Find the dy/dx xy = (x+y) ^4
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Lamont Waller
1 October, 02:10
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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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