求sin(x*(y^2))+secx=e^(x^2)*y的导函数
sin(xy²)+secx=e^(x²)·y
两边对x求导:
cos(xy²)·(y²+2xyy')+secxtanx=e^(x²)·2x·y+e^(x²)·y'
y'[2xycos(xy²)-e^(x²)]=2xye^(x²)-y²cos(xy²)
y'=[2xye^(x²)-y²cos(xy²)]/[2xycos(xy²)-e^(x²)]
两边同时对x求导,得
cos(xy²)*(y²+2xyy')+secxtanx=exp(x²)*2xy+exp(x²)y'
移项,得
y'=[exp(x²)*2xy-cos(xy²)*y²-secxtanx]/[2xy*cos(xy²)-exp(x²)]
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