I\'m reading the book Calculus Made Easy by Silvanus P. Thompson. So far, it\'s

Question

I'm reading the book Calculus Made Easy by Silvanus P. Thompson. So far, it's pretty easy to understand, but there's an example I'm having some difficulty in solving. The particular example is #11 on Chapter VI: Sums, Differences, Products, and Quotients. (You can read the chapter here: http://goo.gl/kaXq5l) (The problem in question is on page 44.)

I would appreciate a step-by-step method on how to solve this problem. I have a feeling I'm either getting the answer, or getting very close to it. Regardless, my answer certainly isn't matching the answer provided in the book, and thus, I would like to know how to get that answer.

Thanks!

Explanation / Answer

theta=1-a*t^(2/3))/(1+a*t^(3/2))

Apply u/v rule

d(u/v) /dt =( v(du/dt) -(u(dv/dt)) /v^2

here v = 1+at^3/2

u = 1-at^2/3

du/dt = 2a/t^1/3

dv/dt = 3at^1/2

d(u/v) /dt =( ((1+at^3/2)(2a/t^1/3)) -((1-at^2/3)3at^1/2))/(1+at^3/2)^2

= (2a/t^1/3 +2a^2 * t^7/6 -3at^1/2 -3a^2 t^7/6 )/(1+at^3/2)^2

= (2a/t^1/3 -3at^1/2-a^2 * t^7/6)/(1+at^3/2)^2

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