What is the derivative of #f(t) = (1/(3t) , t/(5t-4) ) #?

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Answer 1 · 2017-05-22T21:14:02

#dy/dx = ((5t-4)^2)/(12t^2)#

To find the derivative, use the formula:

#dy/dx = (dy"/"dt)/(dx"/"dt)#

First, find #dy/dt#:

#dy/dt = d/dt(1/(3t)) = -1/(3t^2)#

Next, find #dx/dt#:

#dx/dt = d/dt(t/(5t-4))=((5t-4)-5t)/(5t-4)^2 = -4/(5t-4)^2#

Now, use the formula to find #dy/dx#:

#dy/dx = (dy"/"dt)/(dx"/"dt) = (-1/(3t^2))/(-4/(5t-4)^2) = ((5t-4)^2)/(12t^2)#

Final Answer