Question

f(x)=sinx的导数公式f'(x)=cosx怎么推导？

Answer 1

按定义sin'(x)=lim [sin(x+dx)-sin(x)]/dx (dx-->0) 令dx--->0, 则cos(dx)-->1, sin(dx)-->dx ∴sin'(x)=lim [sin(x+dx)-sin(x)]/dx = lim [sin(x)cos(dx)+sin(dx)cos(x)-sin(x)]/dx =lim [sin(x)+dx cos(x)-sin(x)]/dx =cos(x)证毕

Answer 2

(sinx)' =dsinx/dx =[sin(x+dx)]/dx =(sinxcosdx+sindxcosx)/dx =[(sinx)*0+(dx)*cosx]/dx =dx*cosx/dx =cosx

Answer 3

三角函数的两角和