Find f'(x) and simplify. $$f(x) = \frac{x^2+2}{9x-8}$$ Which of the following shows the correct application of the quotient rule? A. $$\frac{(9x-8)(2x) - (x^2+2)(9)}{[9x-8]^2}$$ B. $$\frac{(x^2+2)(9) - (9x-8)(2x)}{[9x-8]^2}$$ C. $$\frac{(9x-8)(2x) - (x^2+2)(9)}{[x^2+2]^2}$$ D. $$\frac{(x^2+2)(9) - (9x-8)(2x)}{[x^2+2]^2}$$ $$f'(x)=$$
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The given function is $$f(x) = \frac{x^2+2}{9x-8}$$. We need to find the derivative $$f'(x)$$ using the quotient rule. The quotient rule states that if $$f(x) = \frac{u(x)}{v(x)}$$, then $$f'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2}$$. Step 2: Identify u(x) Show more…
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