赞 草上飞飞 幼苗
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(sinx)^y=(cosy)^x
两边取对数
ln(sinx)^y=ln(cosy)^x
yln(sinx)=xln(cosy)
两边求导：
y'ln(sinx) y/sinx*cosx=ln(cosy) x/cosy*(-siny)*y'
y'ln(sinx) xy'/(sinycosy)=ln(cosy)-y/(sinxcosx)
y'[ln(sinx) x/(sinycosy)]=ln(cosy)-y/(sinxcosx)
y'=[ln(cosy)-y/(sinxcosx)]/[ln(sinx) x/(sinycosy)]
dy=[ln(cosy)-y/(sinxcosx)]/[ln(sinx) x/(sinycosy)] dx
两边取对数
ln(sinx)^y=ln(cosy)^x
yln(sinx)=xln(cosy)
两边求导：
y'ln(sinx) y/sinx*cosx=ln(cosy) x/cosy*(-siny)*y'
y'ln(sinx) xy'/(sinycosy)=ln(cosy)-y/(sinxcosx)
y'[ln(sinx) x/(sinycosy)]=ln(cosy)-y/(sinxcosx)
y'=[ln(cosy)-y/(sinxcosx)]/[ln(sinx) x/(sinycosy)]
dy=[ln(cosy)-y/(sinxcosx)]/[ln(sinx) x/(sinycosy)] dx
1年前
7
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