函数导数

求方程COSxy=Ex+y -2的确定的隐函数y=y(x)的导数dy/dx

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2019-06-02

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题目表达有不规范之处 cos（xy）=e^(x+y-2） ==> [-sin(xy)]*(y+xy')=e^(x+y-2)*(1+y') ==> [e^(x+y-2)+x*sin(xy)]*y'=-[e^(x+y-2)+y*sin(xy)] ==> dy/dx=y'=-[e^(x+y-2)+y*sin(xy)]/[e^(x+y-2)+x*sin(xy)] 或者也可以将e^(x+y-2)=cos(xy)代入得到更简洁的形式 dy/dx=-[1+y*tan(xy)]/[1+x*tan(xy)]。
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2019-06-02

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求方程COSxy=Ex+y -2的确定的隐函数 y=y(x)的导数dy/dx cosxy=e^(x+y)-2 ===> -sin(xy)*(y+xy')=e^(x+y)*(1+y') ===> -ysin(xy)-xsin(xy)*y'=e^(x+y)+e^(x+y)*y' ===> [e^(x+y)+x*sin(xy)]*y'=-[e^(x+y)+y*sin(xy)] ===> dy/dx=y'=-[e^(x+y)+y*sin(xy)]/[e^(x+y)+x*sin(xy)]。
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