Product Rule Derivative Problem

1. Nov 3, 2012

Burjam

1. The problem statement, all variables and given/known data

Use the product rule to differentiate the function:

h(t) = √t(1-t2)

2. Relevant equations

d/dx[f(x)g(x)] = f(x)g'(x) + g(x)f'(x)

3. The attempt at a solution

(see attachment image)

I checked the back of the textbook and my solution was wrong. The textbook says the answer is (1 - 5t2)/(2√t). What did I do wrong? How do you get this answer?

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2. Nov 3, 2012

Xishem

Between lines 3 and 4 of your work you incorrectly simplified the first term like this:
$$t^{\frac{1}{2}}(-2t)=-2\sqrt t$$Otherwise, I agree with your work.

Last edited: Nov 3, 2012
3. Nov 3, 2012

Burjam

Ahh good catch. You would then just do (-2t√t)(2√t) and get -4t2. Add that to 1 - t2 on the numerator and you get (1 - 5t2) / 2√t, the correct answer in the textbook. Thanks.