求y=x^sin x+(sin x)^x的导数
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求y=x^sinx+(sinx)^x的导数求y=x^sinx+(sinx)^x的导数求y=x^sinx+(sinx)^x的导数y1=x^sinxlny1=sinx.lnx(1/y1)y1''=cosx.
求y=x^sin x+(sin x)^x的导数
求y=x^sin x+(sin x)^x的导数
求y=x^sin x+(sin x)^x的导数
y1= x^sinx
lny1= sinx.lnx
(1/y1)y1' = cosx.lnx + sinx/x
y1' =[cosx.lnx + sinx/x].x^sinx
y2 = (sinx)^x
lny2= xlnsinx
(1/y2) (y2')= lnsinx + xcotx
y2' = [ lnsinx + xcotx].(sinx)^x
y = y1+y2
y' =[cosx.lnx + sinx/x].x^sinx + [ lnsinx + xcotx].(sinx)^x
y'=(x^sinx)'+(sinx^x)'
(x^sinx)'=e^(sinxlnx) * (sinxlnx)'
= x^sinx*(sinx/x+cosxlnx)
同理(sinx^x)'=sinx^x(lnsinx+xcotx)
y'=x^sinx*(sinx/x+cosxlnx)+sinx^x(lnsinx+xcotx)
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