Use implicit differentiation to find the equation of the tangent line to the curve 𝑥2 + 𝑥𝑦 + 𝑦2 = 3 at the point (1,1).
Question
Solution 1
首先，我们需要对方程 x^2 + xy + y^2 = 3 进行隐式微分。这意味着我们需要对方程的每一部分分别求导。
对于 x^2，它的导数是 2x。 对于 xy，我们需要使用乘法法则，它的导数是 x * dy/dx + y。 对于 y^2，它的导数是 2y * dy/dx。
所以，我们得到的微分方程是 2x + x * dy/dx + y + 2y * dy/dx = 0。
然后，我们需要将 dy/dx 的项集中到一边，其他的项移到另一边。这样我们可以得到 dy/dx = -(2x + y) / (x + 2y)。
现在，我们需要找到点 (1,1) 处的斜率。我们将 x 和 y 都替 Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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