{"id":1042,"date":"2021-03-05T21:25:19","date_gmt":"2021-03-05T21:25:19","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus1\/?post_type=chapter&p=1042"},"modified":"2021-06-07T19:56:56","modified_gmt":"2021-06-07T19:56:56","slug":"introduction-to-implicit-differentiation","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus1\/chapter\/introduction-to-implicit-differentiation\/","title":{"raw":"Introduction to Implicit Differentiation","rendered":"Introduction to Implicit Differentiation"},"content":{"raw":"

What you'll learn to do:\u00a0Use implicit differentiation to find derivatives<\/h2>\r\nWe have already studied how to find equations of tangent lines to functions and the rate of change of a function at a specific point. In all these cases we had the explicit equation for the function and differentiated these functions explicitly. Suppose instead that we want to determine the equation of a tangent line to an arbitrary curve or the rate of change of an arbitrary curve at a point. In this section, we solve these problems by finding the derivatives of functions that define [latex]y[\/latex] implicitly in terms of [latex]x[\/latex].","rendered":"

What you’ll learn to do:\u00a0Use implicit differentiation to find derivatives<\/h2>\n

We have already studied how to find equations of tangent lines to functions and the rate of change of a function at a specific point. In all these cases we had the explicit equation for the function and differentiated these functions explicitly. Suppose instead that we want to determine the equation of a tangent line to an arbitrary curve or the rate of change of an arbitrary curve at a point. In this section, we solve these problems by finding the derivatives of functions that define [latex]y[\/latex] implicitly in terms of [latex]x[\/latex].<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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