((e^{4x^2})/(x^2))^'

解答

(\frac{e ^{4 x^{2}}}{x ^{2}})^{^{'}}

\frac{2 e ^{4 x^{2}} ( 4 x ^{2} - 1 )}{x ^{3}}

求解步骤

(\frac{e ^{4 x^{2}}}{x ^{2}})^{'}

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{( e ^{4 x^{2}} ) ^{^{'}} x ^{2} - ( x ^{2} ) ^{^{'}} e ^{4 x^{2}}}{( x ^{2} ) ^{2}}

(e^{4 x^{2}})^{'} = e^{4 x^{2}} \cdot 8 x

(x^{2})^{'} = 2 x

= \frac{e ^{4 x^{2}} \cdot 8 x x ^{2} - 2 x e ^{4 x^{2}}}{( x ^{2} ) ^{2}}

化简

\frac{e ^{4 x^{2}} \cdot 8 x x ^{2} - 2 x e ^{4 x^{2}}}{( x ^{2} ) ^{2}} : \frac{2 e ^{4 x^{2}} ( 4 x ^{2} - 1 )}{x ^{3}}

= \frac{2 e ^{4 x^{2}} ( 4 x ^{2} - 1 )}{x ^{3}}

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