Find-Z-x-and-Z-y-for-each-of-the-functions-below-a-Z-8x-2-y-14xy-2-5y-2-x-3-b-Z-4x-3-y-2-2x-2-y-3-7xy-5-

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

Find Z_{x} and Z_{y} for each of the functions below

(a) Z = {8 x}^{2} y + {14 xy}^{2} + {5 y}^{2} x^{3}

(b) Z = {4 x}^{3} y^{2} + {2 x}^{2} y^{3} - {7 xy}^{5}

Answered by Tinkutara last updated on 22/Jul/17

(a) Z_{x} = 8 y (2 x) + 14 y^{2} + 5 y^{2} (3 x^{2})

= 16 x y + 14 y^{2} + 15 x^{2} y^{2}

Z_{y} = 8 x^{2} + 14 x (2 y) + 5 x^{3} (2 y)

= 10 x^{3} y + 8 x^{2} + 28 x y

(b) Z_{x} = 4 y^{2} (3 x^{2}) + 2 y^{3} (2 x) - 7 y^{5}

= 12 x^{2} y^{2} - 7 y^{5} + 4 {x y}^{3}

Z_{y} = 4 x^{3} (2 y) + 2 x^{2} (3 y^{2}) - 7 x (5 y^{4})

= - 35 {x y}^{4} + 6 x^{2} y^{2} + 8 x^{3} y

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

i really appreciate sir . God bless you