7. (5 pts) Given that $$ e^{y=}-x^{2}+2 x \sin z=0 $$, find $$ \frac{\partial z}{\partial x} $$ using the implicit differentiation. - This function has four critical points at

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Higgins Ortiz · Accepted Answer

To find $$\frac{\partial z}{\partial x}$$, differentiate the equation $$e^y - x^2 + 2x \sin z = 0$$ with respect to $$x$$, then solve for $$\frac{\partial z}{\partial x}$$ to get $$\frac{\partial z}{\partial x} = \frac{-e^y \frac{\partial y}{\partial x} + 2x - 2 \sin z}{2x \cos z}$$. The critical points cannot be determined without additional information.

7. (5 pts) Given that \( e^{y=}-x^{2}+2 x \sin z=0 \), find \( \frac{\partial z}{\partial x} \) using the implicit differentiation. - This function has four critical points at

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7. (5 pts) Given that \( e^{y=}-x^{2}+2 x \sin z=0 \), find \( \frac{\partial z}{\partial x} \) using the implicit differentiation. - This function has four critical points at

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