隱函數(shù)62x78x+64e70y=41x57y的導(dǎo)數(shù)計(jì)算主要內(nèi)容：本文主要通過鏈?zhǔn)角髮?dǎo)、全微分求導(dǎo)和函數(shù)求導(dǎo)法則，介紹隱函數(shù)62x78x+64e70y=41x57y的導(dǎo)數(shù)計(jì)算的主要過程和步驟?！?鏈?zhǔn)角髮?dǎo)法62x78x+64e70y=41x57y,隱函數(shù)變形有：

62e(78xlnx)+64e70y=41e(57ylnx)兩邊同時(shí)求導(dǎo)有：

62e(78xlnx)*(78lnx+eq\f(78x,x))+64e70y*70y'=41e(57ylnx)*(57y'lnx+eq\f(57y,x)),4836e(78xlnx)*(lnx+1)+4480e70y*y'=2337e(57ylnx)*(y'lnx+eq\f(y,x)),

y'=eq\f(2337e(57ylnx)*eq\f(y,x)-4836e(78xlnx)*(lnx+1),e70y-2337e(57ylnx)lnx),=eq\f(2337e(57ylnx)*eq\f(y,x)-4836e(78xlnx)*(lnx+1),4480e70y-2337e(57ylnx)lnx),=eq\f(2337*x57y*eq\f(y,x)-4836*x78x*(lnx+1),4480e70y-2337*x57ylnx),=eq\f(2337*y*x(57y-1)-4836*x78x*(lnx+1),(4480e70y-2337*x57ylnx))。※.全微分法求導(dǎo)隱函數(shù)變形為：62e(78xlnx)+64e70y=41e(57ylnx)，使用全微分計(jì)算法，有：62e(78xlnx)*(78lnxdx+78dx)+4480*e70ydy=41e(57ylnx)*(57lnxdy+57yeq\f(dx,x)),4836*e(78xlnx)*(lnx+1)dx+4480*e70ydy=2337*e(57ylnx)*lnxdy+2337*e(57ylnx)yeq\f(dx,x)),[4480*e70y-2337*e(57ylnx)*lnx]dy=[2337*e(57ylnx)eq\f(y,x)-4836*e(78xlnx)*(lnx+1)]dx,[4480*e70y-2337*x57y*lnx]dy=[2337*yx(57y-1)-4836*x78x*(lnx+1)]dx,所以：eq\f(dy,dx)=eq\f(2337*yx(57y-1)-4836*x78x*(lnx+1),4480*e70y-2337*x57y*lnx),=eq\f(2337*y*x(57y-1)-4836*x78x*(lnx+1),4480e70y-2337*x57ylnx)?！?函數(shù)求導(dǎo)法設(shè)F(x,y)=62x78x+64e70y-41x57y，則F對x,y的偏導(dǎo)數(shù)有：F'x=62e78xlnx*(78lnx+78)-41e(57ylnx)*eq\f(57y,x)=4836*e78xlnx(lnx+1)-2337*x57y*eq\f(y,x)=4836*x78x*(lnx+1)-2337*y*x(57y-1),F'y=4480*e70y-41e57ylnx*57lnx=4480*e70y-2337*x57y*lnx。此時(shí)所求函數(shù)y對x的導(dǎo)數(shù)有：y'=-eq\f(F'x,F'y)=-eq\f(4836*x78x*(lnx+1)-2337*y*x(57y-1),4480*e70y-2337*x5