Answer to Question #275331 in Calculus for Hafsa Tahsin

Question #275331

Find partial z partial x and partial z partial y for


z ^ 4 - y ^ 2 + x ^ 2 = 6x ^ 2 * y ^ 3 * z ^ 7 .

1
Expert's answer
2022-01-11T19:13:36-0500

z4y2+x2=6x2y3z7z ^ 4 - y ^ 2 + x ^ 2 = 6x ^ 2 y ^ 3 z ^ 7

Taking partial derivate w.r.t xx both side for zz (yy will be treated as constant)

4z3zx0+2x=12xy3z7+42x2y3z6zxzx=12xy3z74z342x2y3z64z^3\frac{\partial z}{\partial x}-0+2x=12xy^3z^7+42x^2y^3z^6 \frac{\partial z}{\partial x}\\ \Rightarrow \frac{\partial z}{\partial x}=\frac{12xy^3z^7}{4z^3-42x^2y^3z^6}

Taking partial derivate w.r.t yy both side for zz (xx will be treated as constant)

4z3zy2y+0=18x2y2z7+42x2y3z6zyzy=12xy3z74z318x2y2z74z^3\frac{\partial z}{\partial y}-2y+0=18x^2y^2 z^7+42x^2y^3z^6 \frac{\partial z}{\partial y}\\ \Rightarrow \frac{\partial z}{\partial y}=\frac{12xy^3z^7}{4z^3-18x^2y^2 z^7}

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