Calculus 3 Implicit Differentiation

Question

Calculate the derivative using implicit differentiation:

x⁴w + w⁸ + wz² + 9yz = 0

dw/dz = 

Answer 1

Hello Barbara!

Treat the x's and y's as constants. Also, when you differentiate w, attach "dw/dz" with it:

x⁴(dw/dz)+8w⁷(dw/dz)+z²(dw/dz)+2zw+9y=0

From algebra, (isolate the dw/dz terms on one side and factor out dw/dz)

dw/dz=-(2zw+9y)/(8w⁷+z²+x⁴)

To check, there's a property that states: -F_z/F_w=dw/dz. Try and it works!

I hope this helps!