Constant Multiple Rule...Yes or No?

Find s'(t).

Does the constant multiple rule apply here?

s(t) = [-2(2-t) * sqrt{1+t}]/3

I pulled out 1/3 but my answer is nothing like the book's answer.

Applying the constant rule, the problem now looks like this:

s(t) = (1/3) times [-2(2-t) * sqrt{1+t}]

The fraction (1/3) comes along for the ride.

I then know to apply the product rule to everything else.

The answer is (t)/sqrt{1+t}. Can someone work out this problem for me? I would love to see the steps. I never post a question in this forum without working out the problem many times on my own. Please, help. Thank you.

Re: Constant Multiple Rule...Yes or No?

Yes the constant multiple rule applies here, in fact, it would be easiest if you take out -2/3 as a factor.

Re: Constant Multiple Rule...Yes or No?

I will try this on my own one more time. I never like giving up.

Re: Constant Multiple Rule...Yes or No?

My answer:

(-t)/[2(sqrt{1+t})

The book's answer:

(t)/sqrt{1+t}

I came close but not right. Can you solve this one step by step? Thanks again.

Re: Constant Multiple Rule...Yes or No?

Ok, so you apply the product rule to .

You should get . The first term you can multiply top and bottom by to get in the denominator, and the second will have it when you take the derivative. So what does each term have in the numerator?

- Hollywood

Re: Constant Multiple Rule...Yes or No?

I'll try this one again tomorrow (my day off). I am going chapter by chapter in my single variable calculus text which covers calculus 1 and 2. I always wanted to learn calculus 1-3. Why take out a loan and run myself into debt?

The internet makes it possible for me to learn calculus.

If I can go as far as mutivariable calculus on my own and learn it sufficiently well, it is a great accomplishment. The next chapter is Implicit Differentiation.