How to do the following question?

  1. How to find: given #A = x sqrt(100 - x^2)# and #dx/dt# = 0.3, the valuue of #(dA)/dt# when x = 8 is?

  2. A particle is moving along a curve with equation #y=x^2#. If #dx/dt = 2# at #x = 3#, find #dy/dt# at that instant.

1 Answer
F. Javier B.
Jul 6, 2018

Take into account that #(dA)/dt=(dA)/dx·dx/dt# (chain rule)

So, there is a functional relationship between x and t. In this case is linear

1) Then #(dA)/dx=sqrt(100-x^2)-(x^2)/(sqrt(100-x^2)# at #x=8# his value is #(dA)/dx=6-64/6=-14/3#

#(dA)/dt=(dA)/dx·dx/dt=-14/3·0.3=-7/5# at #x=8#

2) By the same reason above, #(dy)/dt=(dy)/dx·(dx)/dt=2x·2=12# at #x=3#

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