Find $dy over dx$ in the following :
x³ + x² y + x y² + y³ = 81

Here space straight x cubed space plus space straight x to the power of 2 space end exponent straight y space plus space straight x space straight y squared space plus space straight y to the power of 3 space end exponent equals space 81 Differntiating space both space sides space straight w. straight r. straight t space straight x comma space we space get comma space space space space space space space space straight d over dx left parenthesis straight x cubed right parenthesis plus straight d over dx left parenthesis straight x squared straight y right parenthesis plus straight d over dx left parenthesis xy squared right parenthesis plus straight d over dx left parenthesis straight y cubed right parenthesis equals straight d over dx left parenthesis 81 right parenthesis therefore space space space space 3 straight x squared plus straight x squared dy over dx plus straight y.2. straight x plus straight x.2 straight y dy over dx plus straight y squared.1 plus 3 straight y squared dy over dx equals 0 therefore space space space space left parenthesis straight x squared plus 2 xy plus 3 straight y squared right parenthesis dy over dx equals negative left parenthesis 3 straight x squared plus 2 xy plus straight y squared right parenthesis therefore space space space space space space space space space space space space space dy over dx equals negative open parentheses fraction numerator 3 straight x squared plus 2 xy plus straight y squared over denominator straight x squared plus 2 xy plus 3 straight y squared end fraction close parentheses.

90 Views

Continuity and Differentiability

Hope you found this question and answer to be good. Find many more questions on Continuity and Differentiability with answers for your assignments and practice.

Mathematics Part I

Browse through more topics from Mathematics Part I for questions and snapshot.

Find in the following :x3 + x2 y + x y2 + y3 = 81

Continuity and Differentiability

Mathematics Part I

Find $dy over dx$ in the following :
x³ + x² y + x y² + y³ = 81