University:
Rice University
Course:
MATH 212 | Multivariable Calculus
Academic year:

2023
Views:

81

Pages:

2
Author:

Awayne

Implicit Differentiation Until this point, we have been taking the orders of equations whose variables x and y are explicitly defined. There are also implicit equations, situations where the relationship between x and y is implied. In math not only curves but also circles are defined by means of an equation with explicitly given variables x and y. When we find slope, it's always change in y over change in x. So the derivative of x square, not a problem. That's 2x. But how do I take the derivative of y squared? Here, we'll assume that y is a function of x and therefore use the chain rule to find its derivative. We can take the derivative of something squared by taking the derivative of x and then multiplying it by something. So, whenever you differentiate a y term, treat it as if it were an x. The derivative will be the same as long as you multiply by dydx. For example, if you differentiate 9, you get 0. The instructions are to find dydx. If we isolate dydx, we have an answer. So let's subtract 2x from both sides. 2y dydx equals negative 2x. We divide by 2y to get that dydx equals negative 2x divided by 2y . This formula indicates that the slope of this curve is dependent on both x and y coordinates, which are needed in order to determine the slope of this curve, but since we have all x coordinates here, this formula is equal to negative x over y for this curve.