The discussion revolves around understanding the derivatives dy/dt and dx/dt in the context of finding dy/dx, given the equations y=2t+3 and x=t^2. Participants are exploring the relationships between these variables and the process of differentiation.
The discussion is ongoing, with participants seeking clarification on the definitions and implications of dy/dt and dx/dt. Some guidance has been offered regarding the differentiation process, but there remains a lack of consensus on the conceptual understanding of these terms.
Participants express confusion regarding the textbook explanations of derivatives and their meanings, indicating a need for simpler interpretations. There is also a mention of the relationship between dependent and independent variables in differentiation.
Well, look at each equation in turnAllanW said:Homework Statement
if y=2t+3 and x=t^2, find dy/dx
Homework Equations
dy=dy/dt*dt/dx
The Attempt at a Solution
dy/dt=2
dx/dt=2t
therefore dy/dx=1/t
what I don't understand is how the dy/dt etc. is found when attempting this problem[/B]
Do you know how to differentiate the formula 2t+3 with respect to t?AllanW said:what I don't understand is how the dy/dt etc. is found when attempting this problem
It is the rate of increase of y as t increases. Loosely put, it is the size of the tiny increase in y that would arise from making a tiny increase to t and putting that in the formula for y. If you do a line graph of y on the vertical axis against t on the horizontal axis it is the slope (gradient) of the line.AllanW said:i suppose what I am asking would be; what does dy/dt mean