y=x+sinx
y'=1+cosx>=0,
因此y單調(diào)增,所以存在反函數(shù)
交換x,y,得反函數(shù)y=f^(-1)(x)滿足：
x=y+siny
對x求導(dǎo)：1=y'+y'cosy,得;y'=1/(1+cosy)
x=1時,由1=y+siny,得：y=y0
因此y'(1)=1/(1+cosy0)就是解不出y0才問的……冒似出題應(yīng)該求的是y'(0),這樣的話y(0)=0, 則y'(0)=1/(1+cos0)=1/2如果求的是y'(1),得用數(shù)值解法求得y0=0.51097342938857...y'(0)=0.53411131613025...
證明f(x)=x+sinx一定存在反函數(shù)f^-1(x),并求(f^-1)'(1)
證明f(x)=x+sinx一定存在反函數(shù)f^-1(x),并求(f^-1)'(1)
數(shù)學(xué)人氣：644 ℃時間：2019-10-24 08:56:22
優(yōu)質(zhì)解答
我來回答
類似推薦
- 函數(shù)f(x)=sinx,x∈(π/2,3π/2),f^-1(x)求反函數(shù)
- 求反函數(shù),f(x)=3+sinx
- 函數(shù)f(x)=sinx(π/2≤x≤3π/2)的反函數(shù)
- 證明：若函數(shù)Y=F(X)是奇函數(shù),且存在反函數(shù)X=F'(Y),則此反函數(shù)也是奇函數(shù)
- 若g(x),f(x)互為反函數(shù),則g(f(x))=x.如何證明啊?
- 函數(shù)f(x)=sinx-cosx^2的最小值是?
- 英語翻譯
- I took my grandpa to the hospital this morning,_____ I missed the first class.
- So crazy
- 方差是各個數(shù)據(jù)與平均數(shù)之差的平方的平均數(shù)
- 函數(shù)y=f(x)與它反函數(shù)y=f^-1(x)怎么讀?
- These are photos of my families.Look at them 改錯
猜你喜歡
- 1平面與平面重合,是否屬于平行一類?那重合的兩直線,也屬于平行一類的嗎?
- 2非洲每年因饑餓死亡的人數(shù)及現(xiàn)在饑餓人口數(shù)量拜托各位了 3Q
- 3decide to do sth.還=什么
- 4(7/8)o you think of london?B:5.____london is one of the liveliest cities
- 5啤酒可以托運嗎
- 6邊長為2√6的等邊三角形的中心到一邊的距離為?
- 7please give your hand to help me
- 8已知2的X次方等于3的Y次方等于6的Z次方不等等于1,證明X分之一加Y分之一等于Z分之一.
- 9幫我做做?
- 10機(jī)械分析天平TG628A的使用說明書
- 11in winter ,we wear warm coats to protect our bodies_.
- 12( )was most importance to her ,she told me,was her family it this what as