1.y=x^tanx
兩邊取自然對數(shù)得
lny=tanxlnx
兩邊對x求導(dǎo)得
y'/y=sec^2xlnx+tanx/x
y'=(sec^2xlnx+tanx/x)y=(sec^2xlnx+tanx/x)*x^tanx
2.cos(xy)=x-y,隱函數(shù),兩邊求導(dǎo)
-sin(xy)*(xy)'=1-y'
-sin(xy)*(y+xy')=1-y'
-ysin(xy)-xcos(xy)*y'=1-y'
y'[1-xsin(xy)]=1+ysin(xy)
y'=[1+ysin(xy)]/[1-xsin(xy)]
也可用設(shè)二元函數(shù)f(x,y)=cos(xy)-x+y
用隱函數(shù)求導(dǎo)法:f'x(x,y)+f,y(x,y)*y'=0
f'x(x,y)=-sin(xy)*(xy)'-1
=-ysin(xy)-1
f'y(x,y)=-sin(xy)*(xy)'+1
=-xsin(xy)+1
∴[-ysin(xy)-1]+[-xsin(xy)+1]*y'=0
y'=-[ysin(xy)-1]/[-xsin(xy)+1]
y'=[1+ysin(xy)]/[1-xsin(xy)]