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

Question

Mathematics

Alyvia Acosta

30 May, 07:03

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

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Answers (1)

Know the Answer?

Ariel Perez · Answer 1

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)