正弦函数用定义求导就是用定义来求 F(x)=Sin(x)F'(x)=Lim h->0 ( (F(x+h)-F(x))/h
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正弦函数用定义求导
就是用定义来求 F(x)=Sin(x)
F'(x)=Lim h->0 ( (F(x+h)-F(x))/h )
就是用定义来求 F(x)=Sin(x)
F'(x)=Lim h->0 ( (F(x+h)-F(x))/h )
lim h->0 (sin(x+h)-sin(x))/h
=(sin(x)cos(h)+cos(x)sin(h)-sin(x))/h
由lim h->0 sin(h)/h=1,cos(h)=1-2sin^2(h/2)带入有:
=(sin(x)(1-2sin^2(h/2))+cos(x)*h-sin(x))/h
=(cos(x)*h-2sin(x)*sin^2(h/2))/h
又由lim h->0 sin(h/2)/(h/2)=1得
=cos(x)-2sin(x)*2*h/2
=cos(x)-2sin(x)*h
lim h->0,
所以原式
=cos(x)
=(sin(x)cos(h)+cos(x)sin(h)-sin(x))/h
由lim h->0 sin(h)/h=1,cos(h)=1-2sin^2(h/2)带入有:
=(sin(x)(1-2sin^2(h/2))+cos(x)*h-sin(x))/h
=(cos(x)*h-2sin(x)*sin^2(h/2))/h
又由lim h->0 sin(h/2)/(h/2)=1得
=cos(x)-2sin(x)*2*h/2
=cos(x)-2sin(x)*h
lim h->0,
所以原式
=cos(x)
正弦函数用定义求导就是用定义来求 F(x)=Sin(x)F'(x)=Lim h->0 ( (F(x+h)-F(x))/h
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