Solve g(x, y) = xy^2

Simplify

g (x, y) = x y^{2}

Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x

g_{x} = \frac{\partial}{\partial x} (x y^{2})

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

g_{x} = y^{2} \times \frac{\partial}{\partial x} (x)

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

g_{x} = y^{2} \times 1

Solution

g_{x} = y^{2}

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