Implicit functions

If you were asked to differentiate the following.

{x^3} - 5{y^4} = 7{x^2} - 3y + 6 \\

\sin 2y + {x^2} = 2\cos y - 3xy \\

3{e^{2y}} + 2{x^3} = 3{y^2} - 7\ln y - 5x

These are functions of the form f(x,y) = g(x,y) and are called implicit functions.

In the first tutorial I show you how to find dy/dx for such functions.

\text{Find } \dfrac{dy}{dx} \text{ for the following:}

  1. {x^3} - 5{y^4} = 7{x^2} - 3y + 6

Example using the product rule

Sometimes you will need to use the product rule when differentiating a term.

\text{Find } \dfrac{dy}{dx} \text{ for the following:}

  1. 5x - 3{x^2}{y^4} = 2y - {x^3} + 1




2018-08-08T21:18:16+00:00
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