Product Rule Derivative Problem

[Burjam]

Homework Statement

Use the product rule to differentiate the function:

h(t) = √t(1-t²)

Homework Equations

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

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?

 

[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.

 

[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.