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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


x'_y(0,0)=-1

x'_z(0,0)=-1

Solution

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