# Derivative of a square root fraction. HELP!

by curlybit89
Tags: derivative, fraction, root, square
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 P: 2 1. The problem statement, all variables and given/known data What is f'(x) of f(x) 1/sqrt(2x)? 2. The attempt at a solution In applying the problem to the derivative formula: (1 / sqrt(2(x + h)) - 1 / sqrt(2x)) / h I multiplied the problem by a special form of one but that only put the rationals on the bottom of the division. This looked too messy. Alternatively, multiplying each side of the first division by it's denominator yielded the following: (sqrt(2x) - sqrt(2x2h) / sqrt(2x^2 * 2x * 2h)) / h I'm not sure how to proceed from here. Another alternative I attempted was to use the exponent method which for me yielded: original: 2x^-(1/2) = -(x)^-(3/2) This answer did not seem appropriate.
 P: 723 Think of another way to write the derivate. What is another way to write 1/sqrt(2x) ? Thanks Matt
 P: 19 Easiest solution in my opinion would be to just re-write it as $$(2x)^{-1/2}$$ and simply take the derivative of that. Don't forget it is f'(x)=n*$$(u)^{n-1}$$ *u'
P: 286
Derivative of a square root fraction. HELP!

 Quote by curlybit89 1. The problem statement, all variables and given/known data What is f'(x) of f(x) 1/sqrt(2x)? 2. The attempt at a solution [snip] Another alternative I attempted was to use the exponent method which for me yielded: original: 2x^-(1/2) = -(x)^-(3/2) This answer did not seem appropriate.
You are almost correct here.

$$\frac{1}{\sqrt{2x}} = (2x)^{-1/2}$$

$$\frac{d}{dx}\left( (2x)^{-1/2} \right) = -\frac{1}{2}(\bold{2}x)^{-3/2}(2)$$

Proceed from there...

--Elucidus
HW Helper
P: 1,422
 Quote by curlybit89 1. The problem statement, all variables and given/known data What is f'(x) of f(x) 1/sqrt(2x)? 2. The attempt at a solution In applying the problem to the derivative formula: (1 / sqrt(2(x + h)) - 1 / sqrt(2x)) / h I multiplied the problem by a special form of one but that only put the rationals on the bottom of the division. This looked too messy. Alternatively, multiplying each side of the first division by it's denominator yielded the following: ((sqrt(2x) - sqrt(2x + 2h)) / sqrt(2x^2 * 2x * 2h)) / h
You are missing a plus, and a pair of parentheses there.

When solving limit of the Indeterminate Form 0/0, you should try to factorize it. And factorizing the numerator, which contains radicals is impossible, right? So, one should think of a way to rationalize it. How about multiplying both numerator and denominator by

$$\sqrt{2x} + \sqrt{2x + 2h}$$?

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