Find dz/dx?

Question

The equation x-z=arctan(yz) defines z implicitly as a function of x and y. Find dz/dx.

1-dz/dx=(1/(1+(yz)^2))*y*dz/dx

How do I leave dz/dx by itself?

Show me step by step.

Answer 1

x-z=arctan(yz)

1 - (dz/dx) =  (y(dz/dx)/(1 + (yz)^2)

1  =  (dz/dx)((1 +  y/(1 + (yz)^2)))

dz/dx  =  (1 + (yz)^2)/(1 + y + (yz)^2)