Taking Derivatives

[jtw2e2]

This is part of an optimization problem:

A(x) = (1/16)x[sup:2eypuuix]2[/sup:2eypuuix] + (?3/36)(10-x)[sup:2eypuuix]2[/sup:2eypuuix]

I have this but I know my sign is wrong...I just don't know why:

A'(x) = (1/8)x + (?3/18)(10-x)

I really have no understanding about finding the derivative that A(x). I used the power rule on the (1/16)x[sup:2eypuuix]2[/sup:2eypuuix] but didn't really know how to approach the second term. Math gods please help...

 

[Deleted member 4993]

This is part of an optimization problem:

A(x) = (1/16)x[sup:3a6r7yq4]2[/sup:3a6r7yq4] + (?3/36)(10-x)[sup:3a6r7yq4]2[/sup:3a6r7yq4]

I have this but I know my sign is wrong...I just don't know why:

A'(x) = (1/8)x + (?3/18)(10-x)

I really have no understanding about finding the derivative that A(x). I used the power rule on the (1/16)x[sup:3a6r7yq4]2[/sup:3a6r7yq4] but didn't really know how to approach the second term. Math gods please help...

what is f'(x) - when f(x) = 10 - x

 

[jtw2e2]

what is f'(x) - when f(x) = 10 - x

f'(x) would then = -1

I got confused because of the multiplication of those two terms in parentheses. I didn't know if I should use the power rule on the (?3/18) or on the (10-x)... or if the product rule applied since to things were being multiplied?

I don't know fundamental rules for taking derivatives. Of course we went through them in the book, but it seems like we only addressed a tiny fraction of the possibilities that we encounter. Is there somewhere I can go to see a better approach or use of derivation rules?

 

[wjm11]

A(x) = (1/16)x2 + (?3/36)(10-x)2

I have this but I know my sign is wrong...I just don't know why:

A'(x) = (1/8)x + (?3/18)(10-x)

I really have no understanding about finding the derivative that A(x). I used the power rule on the (1/16)x2 but didn't really know how to approach the second term.

The product rule is not necessary here. Only use it if both things you are multiplying together are functions of x. In this case, one of them is just a constant.

After you apply the power rule, you still need to take the derivative of the x function in the parentheses, (10 - x), per the Chain Rule. That is where the "-" comes from.