Question

how to do the derivative of sqrt(t)*(1-t^2)

Answer 1

Use product rule.

Answer 2

\[
(\sqrt{t}(1-t^2))'=(\sqrt{t})'(1-t^2)+(\sqrt{t})(1-t^2)'
\]

Answer 3

after multiplying from both sides. what do I do about the powers.

Answer 4

Differentiate the parts with in \((\ldots )'\)

Answer 5

The parts without \('\) aren't differentiated.

Answer 6

what I have right now is (1-5t^(3/2)/2t^(1/2). does need it to change further?

Answer 7

I'm not really sure how you got that.

Answer 8

What I get is \[
\frac{1-t^2}{2\sqrt{t}}-2t\sqrt{t}
\]

Answer 9

Though I didn't simplify.

Answer 10

Simplifying a step gives\[
\frac{1-t^2-4t^2}{2\sqrt{t}}=\frac{1-5t^2}{2\sqrt{t}}
\]