更新1:
Thank you Bob Williams. I can't believe I forgot my basic differentiation rules. I completely blanked out on that one. Wow...
How do you differentiate xsin(x) ?
回答 (4)
2007-12-05 3:17 am
✔ 最佳答案
Product Rule...x*cos(x) + sin(x)
2007-12-05 11:19 am
xsin(x)
Derivative:
[(deriv of 1st term) * (2nd term) + (1st term) * (deriv of 2nd term)]
[ 1*sin(x) ] + [x *cos(x) ]
Derivative:
[(deriv of 1st term) * (2nd term) + (1st term) * (deriv of 2nd term)]
[ 1*sin(x) ] + [x *cos(x) ]
2007-12-05 11:19 am
you would use the product rule.
xsin(x) you take the derivative of x which is 1 and the derivative of sin(x) which is cos(x)
f=x f'=1
g=sin(x) g'=cos(x)
then you use the formula f(g')+g(f')
so. . . x(cos(x))+sin(x)(1) = xcos(x)+sin(x)
I,KEA
xsin(x) you take the derivative of x which is 1 and the derivative of sin(x) which is cos(x)
f=x f'=1
g=sin(x) g'=cos(x)
then you use the formula f(g')+g(f')
so. . . x(cos(x))+sin(x)(1) = xcos(x)+sin(x)
I,KEA
2007-12-05 11:18 am
by using product rule
d(uv)/dx = udv/dx + vdu/dx
let u = x v = sinx hence du/dx=1 dv/dx = cosx
hence (xsinx)' = xcosx + sinx
d(uv)/dx = udv/dx + vdu/dx
let u = x v = sinx hence du/dx=1 dv/dx = cosx
hence (xsinx)' = xcosx + sinx
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