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Question Number 18469 by tawa tawa last updated on 22/Jul/17

$$\mathrm{Find}{\mathrm{Z}}_{\mathrm{x}}\mathrm{and}{\mathrm{Z}}_{\mathrm{y}}\mathrm{for}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{functions}\mathrm{below}$$$$\left(\mathrm{a}\right)\mathrm{Z}={8\mathrm{x}}^2\mathrm{y}+{14\mathrm{xy}}^2+{5\mathrm{y}}^2{\mathrm{x}}^3$$$$\left(\mathrm{b}\right)\mathrm{Z}={4\mathrm{x}}^3{\mathrm{y}}^2+{2\mathrm{x}}^2{\mathrm{y}}^3-{7\mathrm{xy}}^5$$

Answered by Tinkutara last updated on 22/Jul/17

$$\left(\mathrm{a}\right)Z_x=8y\left(2x\right)+14y^2+5y^2\left(3x^2\right)$$$$=16xy+14y^2+15x^2{y}^2$$$$Z_y=8x^2+14x\left(2y\right)+5x^3\left(2y\right)$$$$=10x^{3}y+8x^2+28xy$$$$\left(\mathrm{b}\right)Z_x=4y^2\left(3x^2\right)+2y^3\left(2x\right)-7y^5$$$$=12x^2{y}^2-7y^5+4{xy}^3$$$$Z_y=4x^3\left(2y\right)+2x^2\left(3y^2\right)-7x\left(5y^4\right)$$$$=-35{xy}^4+6x^2{y}^2+8x^{3}y$$

Commented by tawa tawa last updated on 22/Jul/17

$$\mathrm{i}\mathrm{really}\mathrm{appreciate}\mathrm{sir}.\mathrm{God}\mathrm{bless}\mathrm{you}$$

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