a) For \( y=\frac{5 x+1}{x^{2}+2} \), find \( \frac{d y}{d x} \) Express your answer as a single, simplified fraction.

Find the first order derivative with respect to \( x \) for \( (5*x+1)/(x^2+2) \). Evaluate the derivative by following steps: - step0: Evaluate the derivative: \(\frac{d}{dx}\left(\frac{\left(5x+1\right)}{\left(x^{2}+2\right)}\right)\) - step1: Remove the parentheses: \(\frac{d}{dx}\left(\frac{5x+1}{x^{2}+2}\right)\) - step2: Use differentiation rules: \(\frac{\frac{d}{dx}\left(5x+1\right)\times \left(x^{2}+2\right)-\left(5x+1\right)\times \frac{d}{dx}\left(x^{2}+2\right)}{\left(x^{2}+2\right)^{2}}\) - step3: Calculate: \(\frac{5\left(x^{2}+2\right)-\left(5x+1\right)\times 2x}{\left(x^{2}+2\right)^{2}}\) - step4: Calculate: \(\frac{5\left(x^{2}+2\right)-2x\left(5x+1\right)}{\left(x^{2}+2\right)^{2}}\) - step5: Calculate: \(\frac{-5x^{2}+10-2x}{\left(x^{2}+2\right)^{2}}\) - step6: Calculate: \(\frac{-5x^{2}+10-2x}{x^{4}+4x^{2}+4}\) The derivative of \( y = \frac{5x+1}{x^{2}+2} \) with respect to \( x \) is \( \frac{-5x^{2}+10-2x}{x^{4}+4x^{2}+4} \).