What is (\partial ^2)/(\partial {h)(w)\partial w}(w/({h)(w)(w)^2}) ?

The answer to (\partial ^2)/(\partial {h)(w)\partial w}(w/({h)(w)(w)^2}) is

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(\partial ^2)/(\partial {h)(w)\partial w}(w/({h)(w)(w)^2})

\frac{\partial ^{3}}{\partial h ( w ) \partial w ^{2}} (\frac{w}{h ( w ) ( w ) ^{2}})

- \frac{2 ( 3 w ^{2} \frac{\partial}{\partial w} ( h ( w ) ) ^{2} - w ^{2} h ( w ) \frac{\partial ^{2}}{\partial w ^{2}} ( h ( w ) ) + 2 w h ( w ) \frac{\partial}{\partial w} ( h ( w ) ) + h ( w ) ^{2} )}{w ^{3} h ( w ) ^{4}}

Solution steps

\frac{\partial ^{3}}{\partial h ( w ) \partial w ^{2}} (\frac{w}{h ( w ) ( w ) ^{2}})

\frac{\partial}{\partial h ( w )} (\frac{w}{h ( w ) w ^{2}}) = - \frac{1}{w h ( w ) ^{2}}

= \frac{\partial ^{2}}{\partial w ^{2}} (- \frac{1}{w h ( w ) ^{2}})

\frac{\partial}{\partial w} (- \frac{1}{w h ( w ) ^{2}}) = \frac{h ( w ) + 2 w \frac{\partial}{\partial w} ( h ( w ) )}{w ^{2} h ( w ) ^{3}}

= \frac{\partial}{\partial w} (\frac{h ( w ) + 2 w \frac{\partial}{\partial w} ( h ( w ) )}{w ^{2} h ( w ) ^{3}})

\frac{\partial}{\partial w} (\frac{h ( w ) + 2 w \frac{\partial}{\partial w} ( h ( w ) )}{w ^{2} h ( w ) ^{3}}) = - \frac{2 ( 3 w ^{2} \frac{\partial}{\partial w} ( h ( w ) ) ^{2} - w ^{2} h ( w ) \frac{\partial ^{2}}{\partial w ^{2}} ( h ( w ) ) + 2 w h ( w ) \frac{\partial}{\partial w} ( h ( w ) ) + h ( w ) ^{2} )}{w ^{3} h ( w ) ^{4}}

= - \frac{2 ( 3 w ^{2} \frac{\partial}{\partial w} ( h ( w ) ) ^{2} - w ^{2} h ( w ) \frac{\partial ^{2}}{\partial w ^{2}} ( h ( w ) ) + 2 w h ( w ) \frac{\partial}{\partial w} ( h ( w ) ) + h ( w ) ^{2} )}{w ^{3} h ( w ) ^{4}}

\frac{5 e ^{- s}}{4 s ^{2} + 36}

- 2 cos (\frac{x}{2})

x \to \infty lim (arctan (4 x))

f (x) = ln (3 x + 4), (2, ln (10))

- 5 cos (3 t)

What is (\partial ^2)/(\partial {h)(w)\partial w}(w/({h)(w)(w)^2}) ?
The answer to (\partial ^2)/(\partial {h)(w)\partial w}(w/({h)(w)(w)^2}) is