1. Some derivative questions

Hey guys, I have a couple questions on derivatives, since I just started.

Question 1.

I have a question which said differentiate v=(square root x + 1/3square root)2, I got the derivative eventually, but when I tried chain rule once I learnt it, it gave me a totally different answer? So when it says "differentiate" do I just do all the algebra and eventually get the derivative and then for chain rule I only use it when it says find the derivative?

Question 1.

Derivative of such quantities as 2(x+1), x3(2x+1)

Do I just foil through it, then find the derivative or is it like the chain rule?

Thank you.

2. Re: Some derivative questions

For your first question 1, it's probably simplest to use the chain rule. If you multiply it out and then take the derivative, you should get the same result. If you show us how you got two different answers, we can probably show you where you went wrong. "Differentiate" and "find the derivative" mean exactly the same thing.

For your second question 1, I would multiply them out and then just take the derivative term-by-term. You could use the product rule on the second one, but that's probably harder.

- Hollywood

3. Re: Some derivative questions

Err meant question 2 on that one lol, so for 2(x+1) you're saying just multiply through and find derivative and the x3(2x+1) use product rule, instead of doing the same as the one before? And I'll go over the first question and see where I went wrong with the chain rule unless I was suppose to simplify it even more.

Also if I use x3(2x+1) as a product rule, would I have to treat (2x+1) as g(x) or just the 2x?

4. Re: Some derivative questions

Your answer when applying the chain rule to the first question was probably different because you mixed up the differentiation of the inverse square root.

5. Re: Some derivative questions

For $x^3(2x+1)$ it'll be easier to multiply it through and take the derivative. But if you were to use the product rule, g(x) would be 2x+1.

- Hollywood

6. Re: Some derivative questions

Originally Posted by hollywood
For $x^3(2x+1)$ it'll be easier to multiply it through and take the derivative. But if you were to use the product rule, g(x) would be 2x+1.

- Hollywood

Thank you!!