Let f(t)=300(lnt-e^-4t)^3.Calculate f'(1) accurate to three decimal places.

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- Dec 11th 2009, 05:07 PM #1

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- Dec 11th 2009, 05:26 PM #2
One way to do it is first to calculate the derivative, and then expand the derivative in a power series about some point close to 1. Then use Cauchy's formula for the error term to decide how many terms of the series you need to sum to get that accuracy.

- Dec 12th 2009, 04:38 AM #3

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- Dec 14th 2009, 12:09 PM #4

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## derivative using chain rule?

Am getting stuck at the f'(x)

300(ln t-e^-4t)^3

let ln t -e^-4t=u

1/t+4e^-4t dt = du

dt=t du/1+4e^-4t

hence

300(u)^3 . t du/1+4e^-4t

900u^2 . t du/1+4e^-4t

900(ln t -e^-4t)^2 . t du/1+4e^-4t

but this doesn't seem quite right.Any suggestions?

- Dec 14th 2009, 12:11 PM #5

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