Use implicit differentiation to find ∂z/∂x and ∂z/∂y. x2 + 4y2 + 7z2 = 1 ∂z/∂x = ∂z/∂y =

The required differential functions ∂z/∂x and ∂z/∂y are -2x/14z and -8y/14z

Given the equation:

x² + 4y² + 7z² = 1

Rewriting the equation

x² + 4y² + 7z² - 1 = 0

f(x, y, z) = 0

We are to find the differential equations ∂z/∂x and ∂z/∂y

∂z/∂x means we are to differentiate with respect to x keeping y constant

Differentiating using the implicit differentiation

Recall

x² + 4y² + 7z² - 1 = 0

On differentating with respect to x:

2x + 0 + 14x ∂z/∂x = 0

14z ∂z/∂x = - 2x

14z ∂z/∂x = -2x

∂z/∂x = -2x/14z

Similarly for ∂z/∂y

Differentiating implicitly with respect to y;

0 + 8y + 14z∂z/∂y = 0

14z∂z/∂y = -8y

∂z/∂y = -8y/14z

Hence the required differential functions ∂z/∂x and ∂z/∂y are -2x/14z and -8y/14z

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Assuming , differentiating both sides wrt gives

and wrt gives

5050 i think

step-by-step explanation: