193k views
3 votes
Use implicit differentiation to find ∂z/∂x and ∂z/∂y. x2 + 4y2 + 7z2 = 1 ∂z/∂x = ________ ∂z/∂y = __________

User MetaTron
by
9.0k points

1 Answer

2 votes

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}

User Shankar Gupta
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories