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$x \rightarrow y = g(x) \rightarrow z = f(y) = f(g(x))$

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Chain rule: $ [f(g(x))]' = f'(g(x)) \cdot g'(x)$

\hskip 1.15in ${dz \over dx} = {dz \over dy}{dy \over dx}$

\hskip 0.7in $lim_{\Delta x \rightarrow 0} {\Delta z \over \Delta x} =  lim_{\Delta x \rightarrow 0} {\Delta z \over 
\Delta y} {\Delta y \over \Delta x} $

Examples:

$[cos(e^x + 5x^2)]'=$
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$(x^3 [sin(x^2)][cos(x^{-1} + 5])' =$
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$\big[\sqrt{{ sin(x^{-1}) \over e^{x^2} }}\big]' =$
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$[e^{sin(e^{x^2 + 3x})}]' =$


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