Suppose that a differentiable function (x, y) has the constant value c along the differentiable curve x = g(t), y = h(t); that is, (g(t),

Suppose that a differentiable function ƒ(x, y) has the constant value c along the differentiable curve x = g(t), y = h(t); that is, ƒ(g(t), h(t)) = c for all values of t. Differentiate both sides of this equation with respect to t to show that ∇ƒ is orthogonal to the curve’s tangent vector at every point on the curve.