Monday, November 13, 2017

Calculus and Its Applications, Chapter 1, 1.7, Section 1.7, Problem 56

Determine dydt if y=13u57 and u=7t2+1.

We have dydt=dydududt
with


dydu=(3u57)ddu(1)1ddu(3u57)(3u57)2 and dudt=7ddt(t2)+ddt1=15u4(3u57)2=14t


Thus,


dydt=15u4(3u57)214t=210tu4(3u57)2=210t(7t2+1)4[3(7t2+1)57]2Substitute 7t2+1 for u

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