a.maths question

tom

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?

小妖

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

原帖由 小妖 於 2008-10-22  10:13 PM 發表
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

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

小妖

原帖由 tom 於 2008-10-22  10:24 PM 發表

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

what's difference between your and my answers?

tom

原帖由 小妖 於 2008-10-22  11:46 PM 發表


what's difference between your and my answers?

但係唔知點解兩題個answer同我本書唔同

tom

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

小妖

原帖由 tom 於 2008-10-22  11:55 PM 發表

但係唔知點解兩題個answer同我本書唔同

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

原帖由 小妖 於 2008-10-23  12:11 AM 發表


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