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Question Number 167404 by bharath23 last updated on 15/Mar/22

Answered by alephzero last updated on 15/Mar/22

(∂f/∂x) = (∂/∂x)(y cos xy) = y (∂/∂x)(cos xy)  = y ((∂(cos xy))/(∂(xy))) ∙ ((∂(xy))/∂x) = −y^2  sin xy ■

$$\frac{\partial{f}}{\partial{x}}\:=\:\frac{\partial}{\partial{x}}\left({y}\:\mathrm{cos}\:{xy}\right)\:=\:{y}\:\frac{\partial}{\partial{x}}\left(\mathrm{cos}\:{xy}\right) \\ $$$$=\:{y}\:\frac{\partial\left(\mathrm{cos}\:{xy}\right)}{\partial\left({xy}\right)}\:\centerdot\:\frac{\partial\left({xy}\right)}{\partial{x}}\:=\:−{y}^{\mathrm{2}} \:\mathrm{sin}\:{xy}\:\blacksquare \\ $$

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