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
dy/dt and dx/dt are both mathematical notations used to represent the rate of change of a dependent variable y and an independent variable x, respectively, with respect to time t. They are commonly used in calculus and physics to calculate the instantaneous rate of change of a variable at a specific point in time.
To calculate dy/dt and dx/dt, you need to take the derivative of the function with respect to time t. This can be done using the rules of calculus, such as the power rule or the chain rule. Once you have the derivative, you can substitute the given value of t to find the instantaneous rate of change at that specific point in time.
Dy/dt and dx/dt are commonly used in situations where the rate of change of a variable is continuously changing, such as in motion or growth problems. They are also used in differential equations to describe the relationship between variables and their rates of change.
The main difference between dy/dt and dx/dt is the variable they represent the rate of change for. Dy/dt represents the rate of change of a dependent variable y, while dx/dt represents the rate of change of an independent variable x. However, both notations are used to calculate the instantaneous rate of change at a specific point in time.
Yes, dy/dt and dx/dt can have negative values. This indicates that the variable is decreasing at the given point in time. Positive values indicate an increasing variable, while a value of zero indicates no change. It is important to pay attention to the sign of dy/dt and dx/dt when interpreting the rate of change in a problem.