009A Sample Midterm 3, Problem 5

Find the derivatives of the following functions. Do not simplify.

(a)  Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle f(x)=\sin {\bigg (}{\frac {x^{-3}}{e^{-x}}}{\bigg )}}

(b)  $g(x)={\sqrt {\frac {x^{2}+2}{x^{2}+4}}}$

(c)  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h(x)=(x+\cos^2x)^8}

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