Not understanding simplification of chain rule prob: x times the square root of x-6

[rcdavis28]

The problem is x times the square root of x-6. I rewrote sqr x-6 as x to the 1/2 power and applied the chain and product rules on the problem. The book has the simplified answer as being 3(x-4) / 2(sqr of x-6) . I am just not seeing this. Would someone please be willing to illustrate if the answer is correct?

 

[Deleted member 4993]

The problem is x times the square root of x-6.

I rewrote sqr x-6 as x to the 1/2 power and applied the chain and product rules on the problem. The book has the simplified answer as being 3(x-4) / 2(sqr of x-6) . I am just not seeing this. Would someone please be willing to illustrate if the answer is correct?

The problem is x times the square root of x-6.

You did not tell us what you needed to FIND.

 

[Dr.Peterson]

The problem is x times the square root of x-6. I rewrote sqr x-6 as x to the 1/2 power and applied the chain and product rules on the problem. The book has the simplified answer as being 3(x-4) / 2(sqr of x-6) . I am just not seeing this. Would someone please be willing to illustrate if the answer is correct?

Presumably, since you mention the chain rule and this is under calculus, you want to differentiate the function f(x) = x sqrt(x-6). It's a good idea to say that!

They have done some simplification after applying the product rule. How about if you show us your result, and then we show you how to get from there to their answer?

The main trick will be to factor out a common factor of (x-6)^(-1/2). By the way, note the importance of putting parentheses around the radicand to make it clear.