find dy/dx of :

xy^3 - yx^3 = x

Asked by Krrish2k15 | 25th May, 2019, 10:55: AM

Expert Answer:

xy3 - yx3 = x
begin mathsize 16px style straight x cross times 3 straight y squared dy over dx plus straight y cubed minus open parentheses straight y cross times 3 straight x squared plus straight x cubed dy over dx close parentheses equals 1
3 xy squared dy over dx plus straight y cubed minus 3 straight x squared straight y minus straight x cubed dy over dx equals 1
3 xy squared dy over dx minus straight x cubed dy over dx equals 1 minus straight y cubed plus 3 straight x squared straight y
open parentheses 3 xy squared minus straight x cubed close parentheses dy over dx equals 1 minus straight y cubed plus 3 straight x squared straight y
dy over dx equals fraction numerator 1 minus straight y cubed plus 3 straight x squared straight y over denominator 3 xy squared minus straight x cubed end fraction
end style

Answered by Sneha shidid | 27th May, 2019, 10:13: AM

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