Dick said:A(t)=L(t)W(t), right? Take a look at the 'product rule'. And why would the derivative of L and W be 1?
synergix said:I have really just not been using my brain lately. They would be one if they were being added which they're not. (x + a)'= 2 does it not? if they are both variables.
And you have t in parenthesis to make clear that L and W and A change with time and are therefore not constants right?
so according to the product rule->
dA/dt=L(dW/dt)+W(dW/dt)
Dick said:Because x(t) is a function of t. d(x^1)/dx is 1*x^0 (though you could still throw the chain rule in and write it as 1*x^0*dx/dx, but dx/dx=1). d(x^1)/dt=1*x*dx/dt. dx/dx is always 1. dx/dt is not.
A related rate expanding rectangle is a mathematical concept that involves finding the rate of change of one variable with respect to another variable, typically in the context of a rectangle whose dimensions are changing at different rates.
To find the related rate of an expanding rectangle, you can use the formula dA/dt = lw(dl/dt + dw/dt), where dA/dt represents the rate of change of the area of the rectangle, l and w represent the length and width of the rectangle, and dl/dt and dw/dt represent the rates of change of the length and width, respectively.
Related rate expanding rectangles have many real-life applications, such as in physics (e.g. finding the velocity of a moving object), economics (e.g. determining the marginal cost of production), and engineering (e.g. calculating the rate of expansion of a building due to temperature changes).
Some tips for solving related rate expanding rectangle problems include clearly defining the variables, drawing a diagram to visualize the problem, and using the appropriate formula. It is also important to pay attention to the units of measurement and to differentiate with respect to time.
Yes, there are some limitations to the related rate expanding rectangle model. It assumes that the dimensions of the rectangle are changing at a constant rate, which may not always be the case in real-life situations. Additionally, it only applies to rectangular shapes and may not be applicable to other shapes or objects.