2024/G9/12

$\mathbf {Chapter3Section2}$
${\frac {d}{dx}}[c]=0$
${\frac {d}{dx}}[c\cdot f(x)]=c\cdot {\frac {d}{dx}}[f(x)]$
${\frac {d}{dx}}[f(x)\pm g(x)]={\frac {d}{dx}}[f(x)]\pm {\frac {d}{dx}}[g(x)]$
${\frac {d}{dx}}[a^{x}]=\ln(a)a^{x}$
${\frac {d}{dx}}[e^{x}]=e^{x}$
$\color {Blue}PowerRule$
${\frac {d}{dx}}[x^{n}]=n\cdot x^{n}-1$
$\color {Blue}ProductRule$
${\frac {d}{dx}}[f\cdot {g}]={\frac {d}{dx}}[f]\cdot {g}+{\frac {d}{dx}}[g]\cdot {f}$
$\color {Blue}QuotientRule$
${\frac {d}{dx}}[{\frac {f}{g}}]={\frac {{\frac {d}{dx}}[f]\cdot {g}-{\frac {d}{dx}}[g]\cdot {f}}{g^{2}}}$
$\mathbf {Ex.1}$
a)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://en.wikipedia.org/api/rest_v1/":): {\displaystyle f(x)=x\cdot{e^x}}
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://en.wikipedia.org/api/rest_v1/":): {\displaystyle f^\prime(x)=1\cdot{e^x}+x\cdot{e^x} }