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Questions › DSE › DSE 2008 › Q17
1 markMathematics › Multivariable calculus › Implicit functions, level curves and second-order conditionsHardabout 4 min

DSE 2008 Question 17: Multivariable calculus

Consider the equation xy+yz+zx=kx^{y}+y^{z}+z^{x}=kxy+yz+zx=k, defined for all positive values of x,y,zx,y,zx,y,z, where kkk is a given positive constant. The partial derivative ∂z/∂x\partial z/\partial x∂z/∂x then equals

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Consider the equation x^y+y^z+z^x=k, defined for all positive values of x,y,z, where k is a given positive constant. The partial derivative ∂ z/∂ x then equals (A) -(xz^(x-1)+y^zln y)/(yx^(y-1)+z^xln z) (B) -(yx^(y-1)+z^xln z)/(xz^(x-1)+y^zln y) (C) -(zy^(z-1)+x^yln x)/(xz^(x-1)+y^zln y) (D) -(zy^(z-1)+z^xln z)/(xz^(x-1)+z^xln z)

Also written as: Consider the equation x^y+y^z+z^x=k, defined for all positive values of x,y,z, where k is a given positive constant. The partial derivative d z/d x then equals

Multivariable calculus has come up 32 times in 7 exams since 2007.

What this question tests

This question is on Implicit functions, level curves and second-order conditions, part of Multivariable calculus in Mathematics.

Slopes of level curves and implicit functions, and conditions for optima in two variables.

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Practise Multivariable calculusMore on Implicit functions, level curves and second-order conditions

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Question from the DSE 2008 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.