Consider the surface F(x,y,z) = x^9*z^2 + sin(y^7*z^2) - 8 = 0.

Find the following partial derivatives :
dz/dx
dz/dy

Differentiate both sides with respect to x [with z being a function of x, and y held constant]:
(9x^8 z^2 + x^9 * 2z ∂z/∂x) + cos(y^7 z^2) * 2y^7 z ∂z/∂x = 0
==> 9x^8 z^2 + z(2x^9 + 2y^7 cos(y^7 z^2)) ∂z/∂x = 0
==> ∂z/∂x = -9x^8 z / (2x^9 + 2y^7 cos(y^7 z^2)).
---------------
Differentiate both sides with respect to y [with z being a function of y, and x held constant]:
x^9 * 2z ∂z/∂y + cos(y^7 z^2) * (7y^6 z^2 + 2y^7 z ∂z/∂y) = 0
==> z(2x^9 + 2y^7 cos(y^7 z^2)) ∂z/∂y = -7y^6 z^2 cos(y^7 z^2)
==> ∂z/∂y = -7y^6 z cos(y^7 z^2) / [2x^9 + 2y^7 cos(y^7 z^2)).

I hope this helps!

its the right answer!

Report Abuse