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If $f(x)=e^{x}$ and $g(x)=\log x$, then what is the value of (gof)' $(x)$?
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Let $f(x)=e^{x}, g(x)=\log x$
Consider $($ g of $)(x)=g[f(x)]$
$=\log f(x) \quad($ By defn of $g(x))$
$=\log \left(e^{x}\right) \quad\left(\because f(x)=e^{x}\right)$
$=x \quad(\because \log e=1)$
Consider $($ g of $)(x)=g[f(x)]$
$=\log f(x) \quad($ By defn of $g(x))$
$=\log \left(e^{x}\right) \quad\left(\because f(x)=e^{x}\right)$
$=x \quad(\because \log e=1)$
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