Derivative of Implicit Multivariable Function – Calculate partial derivatives to an equation with an exponential – Exercise 6481

Exercise

Given that the equation

$e^{x+y+z}=(x^2+y^2)\cdot z+1$

Defines the implicit function

$x(y,z)$

Calculate its partial derivatives at the origin

$x'_y(0,0),x'_z(0,0)$

Final Answer

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Solution

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