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derivative - How do i determine the derivative whats the...

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How do i determine the derivative? whats the derivative of f when f(x) = (SQRT 2x) -1 / SQRT 2x I'll help you out ! The first thing you need to think about when you look at this equation is what rules you need to use to take the derivative. I can tell by looking is we're going to need the chain rule and the quotient rule. I'll apply both in the proper order and tell you why and when I use it. STEP NUMBER 1: Rewrite the equation. (2x)^(1/2) - 1 / (2x)^(1/2) We do this so that we can take the derivative of a square root. A square root is just a number raised to the 1/2 power. QUOTIENT RULE: f'(x)g(x) - g'(x)f(x) (Derivative of the top times the bottom minus derivative of the bottom times the top) [(1/2)(2x)^(-1/2)*2x^(1/2)] - [(1/2)(2x)^(-1/2)*(2x^(1/2)-1)) ALL OVER 2x. Why 2x? Because we square the bottom in the in quotient rule. This breaks 2x free of the sqrt. K. Derivative of the top is the first term, the 1 is removed because it is a constant (MEANS IT HAS NO X). Then it is multiplied by the second. If you look at the first [], that entire thing is f'(x)*g(x). The second term is the
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