Question

Define x and y implicitly as differential functions x=f(t), y=g(t), find the slope of the curve x=f(t), y=g(t) at the given value of t
x=√5-(√t), y(t-1)=lny, t=1

Answer 1

It's just finding derivatives ^.^
I trust you can find
\[\large \frac{dx}{dt}\] without difficulty?

Answer 2

yikes... trickier than I thought :(
Maybe you can introduce a new parameter, t-1 instead?

Answer 3

Can you re-write the function using LaTex? I am kind of unsure of what it is..

Answer 4

You need to take the derivative of the function with respect to, \(t\) for both \(x\) and \(y\).
That means \(\frac{dx}{dt}\) and \(\frac{dy}{dt}\)...your slope is therefore \(\huge \frac{\frac{dy}{dt}}{\frac{dx}{dt}}\)

Answer 5

evaluate the slope: \(\huge \frac{\frac{dy}{dt}}{\frac{dx}{dt}}\) at t=1

Answer 6

I think I panicked ^.^