SOLUTION: Hi, I have a problem with the algebra of getting the derivative of: {{{h(x)=x(sqrt(16-x^2))}}} So far I know it uses product and chain rule {{{ (d/dx)(x) (16-x^2)^(1/2) + (x)

Question 1125287: Hi, I have a problem with the algebra of getting the derivative of:
So far I know it uses product and chain rule

From here my work is definetly wrong if I didn't miss any rules:

Put everything over 2 due to the

Then I took out/factored out :

moving the negative down, then I get for a final answer of
which is also

But the answer is actually:
OR
I'm certain by algebra is messed up somewhere, most likely when I factored but I can't find what I did wrong. I'm very confused since my teacher can easily do it in a few steps but I got lost very fast. Any help would be really great if possible!
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Large number of steps to show.

Using the Product Rule, and working through, one of the steps becomes, for derivative,

Simplifying further gives

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