Differentiate:
1. y=(3x^2-5x+2)^5
2. y=(e^-3x)(cos2x) <.............-3x係次方黎
my answer is.
1. 5(3x^2-5x+2)^4(6x-5)
2. e^-3x(-2sin2x-3cos2x)
is that correct?
A.Maths problem (Differentiate)
2008-11-06 3:44 am
回答 (2)
2008-11-06 3:48 am
✔ 最佳答案
Make use of chain rule and product rule to find the differentiation.1. y = (3x2 - 5x + 2)5
dy/dx = d[(3x2 - 5x + 2)5]/d(3x2 - 5x + 2) X d(3x2 - 5x + 2)/dx
dy/dx = 5(3x2 - 5x + 2)4(6x - 5)
2. y = e-3xcos2x
dy/dx = e-3xd(cos2x)/d(2x) X d(2x)/dx + cos2x d(e-3x)/d(-3x) X d(-3x)/dx
dy/dx = -2e-3xsin2x - 3e-3xcos2x = e-3x(-2sin2x - 3cos2x)
So, your answers are all correct.
2008-11-05 20:38:51 補充：
copycat!!! 002抄襲本人之回答，搬字過紙!!!
參考: Myself~~~
2008-11-06 4:02 am
1. y = (3x2 - 5x + 2)5
dy/dx = d[(3x2 - 5x + 2)5]/d(3x2 - 5x + 2) X d(3x2 - 5x + 2)/dx
dy/dx = 5(3x2 - 5x + 2)4(6x - 5)
2. y = e-3xcos2x
dy/dx = e-3xd(cos2x)/d(2x) X d(2x)/dx + cos2x d(e-3x)/d(-3x) X d(-3x)/dx
dy/dx = -2e-3xsin2x - 3e-3xcos2x = e-3x(-2sin2x - 3cos2x)
dy/dx = d[(3x2 - 5x + 2)5]/d(3x2 - 5x + 2) X d(3x2 - 5x + 2)/dx
dy/dx = 5(3x2 - 5x + 2)4(6x - 5)
2. y = e-3xcos2x
dy/dx = e-3xd(cos2x)/d(2x) X d(2x)/dx + cos2x d(e-3x)/d(-3x) X d(-3x)/dx
dy/dx = -2e-3xsin2x - 3e-3xcos2x = e-3x(-2sin2x - 3cos2x)
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