Question

求导 设y(x)由e^(xy) +tan(xy) +2 =y确定， 求dy/dx|

求导
设y(x)由e^(xy) +tan(xy) +2 =y确定， 求dy/dx|x=0
答案等于6，过程是怎样的，解析。

Answer 1

追答

做任务 请采纳我 谢谢了

追问

e^(xy) +tan(xy) +2 =y
两边分别对x 取导数
d{e^(xy) +tan(xy) +2 } /dx = dy/dx 我不知道导......^_^

追答

啥？

dy比dx就是y对x求导

追问

懂了

^_^

Answer 2

e^(xy) +tan(xy) +2 =y
x=0
1 +2 =y
y=3
(0,3)

e^(xy) +tan(xy) +2 =y
(y+ xdy/dx)e^(xy) + (y+ xdy/dx)(sec(xy))^2 = dy/dx
(x.e^xy+ x(sec(xy))^2 -1) dy/dx = -y(e^(xy) + (sec(xy) )^2)
dy/dx = -y( e^(xy) + (sec(xy) )^2) /(x.e^xy+ x.(sec(xy))^2 -1)

dy/dx| (0,3)
=-3( 1 + 1) /(0+ 0-1)
=6

追问

没看懂，解析一下，1+2=y哪来的我都不知道。^_^

追答

e^(xy) +tan(xy) +2 =y
x=0
e^0 +tan0 +2 =y
1 +0+2 =y
y=3
(0,3)

追问

继续解析

我导数课没听-_-||

追答

z1=e^(xy)
dz1/dx
= e^(xy) . d/dx(xy)
= e^(xy) . (x dyd/x + y)

z2=tan(xy)
dz2/dx
= (sec(xy))^2 .d/dx ( xy)
= (sec(xy))^2 .(x dyd/x + y)

e^(xy) +tan(xy) +2 =y
e^(xy) . (x dyd/x + y) +(sec(xy))^2 .(x dyd/x + y) = dy/dx
化简
dy/dx = -y( e^(xy) + (sec(xy) )^2) /(x.e^xy+ x.(sec(xy))^2 -1)

追问

e^(xy) +tan(xy) +2 =y
两边分别对x 取导数
d/dx {e^(xy) +tan(xy) +2 } = d/dx ( y) 我不知道导......^_^

追答

不知道导数的话， 就不应该作这个练习， 等你了解导数后再说吧！