Find the derivative of f(x)=frac{x^{2}+3^{x}}{sqrt{x}} at x=1.

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Step:1 ：Find the derivatives: (g&#x27;(x) = 2x + 3^x ln(3)) and (h&#x27;(x) = frac{1}{2}x^{-1/2})Step:2 ：Apply the quotient rule: (f&#x27;(x) = frac{g&#x27;(x)h(x) - g(x)h&#x27;(x)}{h(x)^2})Step:3 ：Evaluate at x=1: (f&#x27;(1) = frac{2 + 3 ln(3)}{1} = boxed{3 ln(3)})

Answer

Step: 1 ：Find the derivatives: (g&#x27;(x) = 2x + 3^x ln(3)) and (h&#x27;(x) = frac{1}{2}x^{-1/2})Step: 2 ：Apply the quotient rule: (f&#x27;(x) = frac{g&#x27;(x)h(x) - g(x)h&#x27;(x)}{h(x)^2})Step: 3 ：Evaluate at x=1: (f&#x27;(1) = frac{2 + 3 ln(3)}{1} = boxed{3 ln(3)})

Find the derivative of $f(x)=\frac{x^{2}+3^{x}}{\sqrt{x}}$ at $x=1$.

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