Given the surface: z^2=x^2+xy^2z. Find dz/dx
To find dz/dx, we'll use partial differentiation. We'll differentiate the given surface equation with respect to x, while treating y as a constant.
Let's start by differentiating both sides of the equation:
d/dx(z^2) = d/dx(x^2+xy^2z)
Using the chain rule, we can differentiate the left side of the equation as follows:
2z * dz/dx = 2x + y^2z * dz/dx
Now, let's isolate dz/dx:
2z * dz/dx - y^2z * dz/dx = 2x
Factoring dz/dx:
dz/dx * (2z - y^2z) = 2x
Simplifying the expression:
dz/dx = 2x / (2z - y^2z)
So, dz/dx is equal to 2x divided by (2z - y^2z).