Question

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

Answer 1

Assuming
`z=z(x,y)`, differentiating both sides wrt
`x` gives

`2x+14z(\partial z)/(\partial x)=0\implies(\partial z)/(\partial x)=-\frac x{17z}`

and wrt
`y` gives

`8y+14z(\partial z)/(\partial y)=0\implies(\partial z)/(\partial y)=-\frac4{7z}`