Question

Use the equations \[ \frac{\partial z}{\partial x}=-\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial z}} \text { and } \frac{\partial z}{\partial y}=-\frac{\frac{\partial F}{\partial y}}{\frac{\partial F}{\partial z}} \] to find \( \frac{\partial z}{\partial x} \) and \( \frac{\partial z}{\partial y} \). \[ \begin{array}{l} \frac{x^{2}+4 y^{2}+9 z^{2}=1}{\partial x}=\square \\ \frac{\partial z}{\partial y}=\square \end{array} \]

          Use the equations
\[
\frac{\partial z}{\partial x}=-\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial z}} \text { and } \frac{\partial z}{\partial y}=-\frac{\frac{\partial F}{\partial y}}{\frac{\partial F}{\partial z}}
\]
to find \( \frac{\partial z}{\partial x} \) and \( \frac{\partial z}{\partial y} \).
\[
\begin{array}{l}
\frac{x^{2}+4 y^{2}+9 z^{2}=1}{\partial x}=\square \\
\frac{\partial z}{\partial y}=\square
\end{array}
\]

Use the equations

(∂ z)/(∂ x)=-((∂ F)/(∂ x))/((∂ F)/(∂ z)) and (∂ z)/(∂ y)=-((∂ F)/(∂ y))/((∂ F)/(∂ z))

to find (∂ z)/(∂ x) and (∂ z)/(∂ y).

(x^2+4 y^2+9 z^2=1)/(∂ x)=□
(∂ z)/(∂ y)=□

Added by Luisa R.

College Algebra and Trigonometry

Margaret L. Lial, John Hornsby, David I.… 7th Edition

Chapter 4

Instant Answer

Solved by Expert Collin Parker

Step 1

Given the equation: \[ x^2 + 4y^2 + 9z^2 = 1 \] We can define: \[ F(x, y, z) = x^2 + 4y^2 + 9z^2 - 1 \] Show more…

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Use the equations \[ \frac{\partial z}{\partial x}=-\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial z}} \text { and } \frac{\partial z}{\partial y}=-\frac{\frac{\partial F}{\partial y}}{\frac{\partial F}{\partial z}} \] to find \( \frac{\partial z}{\partial x} \) and \( \frac{\partial z}{\partial y} \). \[ \begin{array}{l} \frac{x^{2}+4 y^{2}+9 z^{2}=1}{\partial x}=\square \\ \frac{\partial z}{\partial y}=\square \end{array} \]