Question

Usee implicit differentiation to find ∂z/∂x and ∂z/∂y. x2 + 4y2 + 9z2 = 7

Answer 1

Via the chain rule, we can first take the partial of the relation with respect to
`(\partial )/(\partial x)\left ( x^2 + 4y^2 +9z^2 = 7)`

From the chain rule, we get:


`(\partial )/(\partial x)\left ( x^2 + 4y^2 +9z^2 = 7 \right ) \to 2x +8y(\partial y)/(\partial x) + 18z(\partial z)/(\partial x) = 0`

Then solve for
`(\partial z)/(\partial x)`


`(\partial z)/(\partial x)= -2x - 8y(\partial y)/(\partial x)`

The same can go for
`(\partial z)/(\partial y)` just take the partial with respect to y