求初等函数的导数与微分设y=e^(tan1/x )sin 1/x,求dydy=d(e^tan1/x)sin 1/x+e^(tan1/x )d (sin 1/x)=(e^tan 1/x 乘 1/((cos^2) 1/x)乘 sin (1/x )+e^(tan 1/x) cos 1/x )d(1/x)(这步怎么算的不懂,重点讲一下)=-1/x^2 e^tan1/x (tan1/x sec1
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![求初等函数的导数与微分设y=e^(tan1/x )sin 1/x,求dydy=d(e^tan1/x)sin 1/x+e^(tan1/x )d (sin 1/x)=(e^tan 1/x 乘 1/((cos^2) 1/x)乘 sin (1/x )+e^(tan 1/x) cos 1/x )d(1/x)(这步怎么算的不懂,重点讲一下)=-1/x^2 e^tan1/x (tan1/x sec1](/uploads/image/z/3487279-31-9.jpg?t=%E6%B1%82%E5%88%9D%E7%AD%89%E5%87%BD%E6%95%B0%E7%9A%84%E5%AF%BC%E6%95%B0%E4%B8%8E%E5%BE%AE%E5%88%86%E8%AE%BEy%3De%5E%28tan1%2Fx+%29sin+1%2Fx%2C%E6%B1%82dydy%3Dd%28e%5Etan1%2Fx%29sin+1%2Fx%2Be%5E%28tan1%2Fx+%29d+%28sin+1%2Fx%29%3D%28e%5Etan+1%2Fx+%E4%B9%98+1%2F%28%28cos%5E2%29+1%2Fx%29%E4%B9%98+sin+%281%2Fx+%29%2Be%5E%28tan+1%2Fx%29+cos+1%2Fx+%29d%281%2Fx%29%28%E8%BF%99%E6%AD%A5%E6%80%8E%E4%B9%88%E7%AE%97%E7%9A%84%E4%B8%8D%E6%87%82%2C%E9%87%8D%E7%82%B9%E8%AE%B2%E4%B8%80%E4%B8%8B%29%3D-1%2Fx%5E2+e%5Etan1%2Fx+%28tan1%2Fx+sec1)
求初等函数的导数与微分设y=e^(tan1/x )sin 1/x,求dydy=d(e^tan1/x)sin 1/x+e^(tan1/x )d (sin 1/x)=(e^tan 1/x 乘 1/((cos^2) 1/x)乘 sin (1/x )+e^(tan 1/x) cos 1/x )d(1/x)(这步怎么算的不懂,重点讲一下)=-1/x^2 e^tan1/x (tan1/x sec1
求初等函数的导数与微分
设y=e^(tan1/x )sin 1/x,求dy
dy=d(e^tan1/x)sin 1/x+e^(tan1/x )d (sin 1/x)=(e^tan 1/x 乘 1/((cos^2) 1/x)乘 sin (1/x )+e^(tan 1/x) cos 1/x )d(1/x)(这步怎么算的不懂,重点讲一下)
=-1/x^2 e^tan1/x (tan1/x sec1/x +cos 1/x)dx
3.y=arctane^x -ln根号 e^2x/e^2x+1,求dy/dx一竖 x=1
由于y=arctane^x -1/2(2x-ln (e^2x+1))=arctane^x -x =1/2 ln (e^2x+1),(这一步是怎么算的,看不懂,讲重点讲)
所以 y'=(e^x /(1+e^2x))-1+((e^2x)/(1+e^2x))=(e^x-1)/(1+e^2x) 推出 dy /dx 一竖 x=1 =e-1/1+e^2
4.y=x^tanx +x^x^x 求y'
这是两个幂指函数之和的求导,先将它表成指数函数的复合函数,然后再用复合函数求导法求导,于是
y=e^tan xln x +exlnx lnx ( 这步是怎么算的,表重点讲)
y'=tanxlnx ((sec^2)xlnx+tanx/x )+e^(e^xlnx)(1+lnx )lnx +(e^xlnx )1/x)
=x^tanx ((sec ^2)xlnx+tanx/x )+x^x^x((ln^2)x+lnx +1/x)
求初等函数的导数与微分设y=e^(tan1/x )sin 1/x,求dydy=d(e^tan1/x)sin 1/x+e^(tan1/x )d (sin 1/x)=(e^tan 1/x 乘 1/((cos^2) 1/x)乘 sin (1/x )+e^(tan 1/x) cos 1/x )d(1/x)(这步怎么算的不懂,重点讲一下)=-1/x^2 e^tan1/x (tan1/x sec1
幂指函数的求导方法要用对数求导法.
对书上的结果,如非很经典的书,通常也会有错.
录入的解答不容易分辨,用照片看我的解答吧,
你还是找本高数书从基础看起吧。
http://wenku.baidu.com/search?word=%CD%AC%BC%C3%B8%DF%B5%C8%CA%FD%D1%A7%B5%DA%C1%F9%B0%E6&lm=0&od=0
我还不太会用。刚才只让插入一个图片,现在再补插入一个第4题的图片。