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)

Algebra ->  Test -> 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)       Log On


   

Question 1125287: Hi, I have a problem with the algebra of getting the derivative of: h%28x%29=x%28sqrt%2816-x%5E2%29%29
So far I know it uses product and chain rule


From here my work is definetly wrong if I didn't miss any rules:
+%2816-x%5E2%29%5E%281%2F2%29%2B%28-2x%5E2%29%28%281%2F2%29%2816-x%5E2%29%5E%28-1%2F2%29%29+
Put everything over 2 due to the %281%2F2%29

Then I took out/factored out :

moving the negative down, then I get for a final answer of
%281-2x%5E2%29%2F+2%28%2816-x%5E2%29%5E%281%2F2%29%29+ which is also +%281-2x%5E2%29%2F+2sqrt%2816-x%5E2%29

But the answer is actually:
%28-2x%5E2-16%29%2F2sqrt%2816-x%5E2%29%29 OR -2%28x%5E2-8%29%2F2sqrt%2816-x%5E2%29
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) About Me  (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,
sqrt%2816-x%5E2%29-x%5E2%2Fsqrt%2816-x%5E2%29


Simplifying further gives
%2816-2x%5E2%29%2Fsqrt%2816-x%5E2%29