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# 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

$$z'_x(3,3,0)=1$$

$$z'_y(3,3,0)=-1$$

Solution

Coming soon…

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