Derivatives and sq. roots: 2 questions

[yanarains]

Well, I understand how to do these types of problems Its just When they involve sq. roots they throw me off track. I guess I just don't understand why and how they become a fraction.

1) Find an equation for a normal line at (1, 1) when given the curve y=2/x-sq.root x;

2) Find the 2nd derivative of y=2/3x - sq.root 2x + sq.root 2x - 1/6sq.root x

could someone please show me step by step how to solve these problems.

All help is greatly appreciated. I have not posted any work because I am not sure exactly where to start with these type of problems. thanks again.

 

[galactus]

Is this what you mean?:

\(\displaystyle \L\\\frac{2}{x-\sqrt{x}}\)

or

\(\displaystyle \L\\\frac{2}{x}-\sqrt{x}\)

I assume the former, but please use proper grouping symbols.

quotient rule:

\(\displaystyle \L\\\frac{(x-\sqrt{x})(0)-(2)(1-\frac{1}{2\sqrt{x}})}{(x-\sqrt{x})^{2}}\)

The normal line is the perpendicular to the line tangent at the point (1,1).

Find the slope at (1,1) and take the negative reciprocal to find the slope of the normal.

Don't let radicals trip you up. Rewrite them as \(\displaystyle x^{\frac{1}{2}}\), then just use the power rule.

 

[stapel]

Well, I understand how to do these types of problems Its just When they involve sq. roots they throw me off track....

Then convert the square root to the one-half power, and proceed as usual. :idea:

could someone please show me step by step how to solve these problems.

I'm sure you have plenty of step-by-step worked examples in your textbook and in your class notes. If you're having trouble anyway, then another step-by-step example probably won't help much.

Instead, please reply showing what you have tried. In this way, the tutors will be able to "see" where you're having trouble, and will be able to try to give you the specific help you need. :wink:

Please be complete. Thank you!

Eliz.