Find its derivative

👨🏻‍🏫 學術台數學

Green1114

2009-07-25 8:12 am

f(x) = x*cosx*sinx
Find its derivative plx , becoz I don't know how to apply product rules.

更新1:

Nevertheless , does product avaiblie when we apply it to product of 3?

回答 (2)

螞蟻雄兵

2009-07-25 8:34 am

✔ 最佳答案

f(x) = x*cosx*sinx ,Find its derivative
Sol
f'(x)=df(x)/dx
=(1/2)d(xsin2x)/dx
=(1/2)xdsin2x/dx+(1/2)sin2xdx/dx
=(x/2)(dsin2x/d2x)*(d2x/dx)+sin2x/2
=xcos2x+sin2x/2

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用戶10012

2009-07-25 2:42 pm

For product of 3, product rule still holds.
Let y = uvw, then y' = uvw' + vwu' + uwv'. [This is derived from y = (uv)w' + w(uv)']

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