kweig said:Homework Statement
So I'm trying to find dy/dt. I used the chain rule to find dx/dt. I just don't understand how to put that answer back into an equation to find dy/dt
Homework Equations
4x^3-6xy^2+3y^2=228
The Attempt at a Solution
I found dx/dt=3 x=-3 and y=4
So how/what equation do I use to find dy/dt
kweig said:The implicit differentiation?
kweig said:I got dy/dt=(2x^2-y^2)/(y(2x-1))
The purpose of evaluating derivatives is to find the rate of change of a function at a specific point. It allows us to understand how the function is changing and can be used to predict future values of the function.
To evaluate a derivative, you need to use the derivative rule or formula for the specific type of function. This may involve taking the limit, finding the derivative of each term, or using the chain rule. Once you have applied the appropriate rule, you can plug in the given value to find the derivative at that point.
A derivative is the instantaneous rate of change of a function at a specific point. It is a single value. A derivative function, on the other hand, is a function that represents the derivative at each point of the original function. In other words, it is a function that gives the slope of the original function at any given point.
Understanding derivatives is important for various reasons. It is a fundamental concept in calculus and is used in many applications such as physics, engineering, economics, and statistics. It allows us to analyze the behavior of functions and make predictions. Additionally, derivatives are crucial in optimization problems, which are commonly encountered in many fields.
Some common applications of derivatives include finding maximum and minimum values of a function, calculating velocity and acceleration in physics, determining marginal cost and revenue in economics, and analyzing the growth of populations in biology. Derivatives are also used in optimization problems, curve sketching, and in many other areas of mathematics and science.