tom 發表於 2008-10-22 20:53:12

a.maths question

evaluate the first derivative of the following functions
y=3xSin(x)cos(x)

if dy/dx given
x=sin(t),y=cos(t)

大家識唔識?:icon102:

小妖 發表於 2008-10-22 22:13:39

1.
dy/dx
=3sinxcosx+3xcosxcosx+3xsinx(-sinx)
=3sinxcox+3x(cosx)^2-3x(sinx)^2
=3/2sin(2x)+3cos(2x)

2.
x=sin(t)
dx/dt=cos(t)

y=cos(t)
dy/dt=-sin(t)

dy/dx
=(dy/dt)/(dx/dt)
=-sin(t)/cos(t)
=-sin(t)/(1-(sin(t))^2)^1/2
=-x/(1-x^2)^1/2

有錯請指教

tom 發表於 2008-10-22 22:24:00

原帖由 小妖 於 2008-10-2210:13 PM 發表 http://hkcmforum.com/images/common/back.gif
1.
dy/dx
=3sinxcosx+3xcosxcosx+3xsinx(-sinx)
=3sinxcox+3x(cosx)^2-3x(sinx)^2
=3/2sin(2x)+3cos(2x)

2.
x=sin(t)
dx/dt=cos(t)

y=cos(t)
dy/dt=-sin(t)

dy/d
=(dy/dt)/(dx/dt)
=-sin(t)/cos(t)
=-sin(t)/(1- ...
no.2個題 answer係 -tan(x)
用Parametric and loagrithmic differentiation

tom 發表於 2008-10-22 22:27:15

no.1個題用product rule and chain rule
唔好e思無講

小妖 發表於 2008-10-22 23:46:52

原帖由 tom 於 2008-10-2210:24 PM 發表 http://hkcmforum.com/images/common/back.gif

no.2個題 answer係 -tan(x)
用Parametric and loagrithmic differentiation

what's difference between your and my answers? :confused:

tom 發表於 2008-10-22 23:55:11

原帖由 小妖 於 2008-10-2211:46 PM 發表 http://hkcmforum.com/images/common/back.gif


what's difference between your and my answers? :confused:
但係唔知點解兩題個answer同我本書唔同:confused:

tom 發表於 2008-10-22 23:58:53

no.1個題
3xSinx(-sinx)+cosx(3x)(cosx)
做到呢到唔識

小妖 發表於 2008-10-23 00:11:54

原帖由 tom 於 2008-10-2211:55 PM 發表 http://hkcmforum.com/images/common/back.gif

但係唔知點解兩題個answer同我本書唔同:confused:

如果講第二題既話

dy/dx
=-sin(t)/cos(t)
=-tan(t)

咁就同你個答案一樣

第一題
個題目其實係唔係
y=3sinxcosx ?

如果係咁就
dy/dx
=3(sinx)(-sinx)+3(cosx)(cosx)
=3(cosx)^2-3(sinx)^2
=3/2cos2x

我以為第一個"x"係x, 唔係乘號

tom 發表於 2008-10-23 00:20:03

原帖由 小妖 於 2008-10-2312:11 AM 發表 http://hkcmforum.com/images/common/back.gif


如果講第二題既話

dy/dx
=-sin(t)/cos(t)
=-tan(t)

咁就同你個答案一樣

第一題
個題目其實係唔係
y=3sinxcosx ?

如果係咁就
dy/dx
=3(sinx)(-sinx)+3(cosx)(cosx)
=3(cosx)^2-3(sinx)^2
=3/2cos2x

我以為第一 ... 第二題第一個係x唔係乘號
但係個answer前面有負
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