Derivative of Implicit Multivariable Function – Calculate partial derivatives to an equation with fractions – Exercise5498

Exercise

Given the implicite function

$1=\frac{y}{x}+\frac{xz}{y^2}+\frac{yz^3}{x^4}$

1. Check that the point

$(3,3,0)$

Holds the equation.

2. Calculate its derivatives

$z'_x, z'_y$

At this point.

Final Answer

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Solution

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