求导:(1)y=(sinx^n)*(cosnx) (2)y=arctan(1/2tanx/2)(1)n(sinx^n-1)cos(n+1)x(2)1/[1+3cos(x/2)^2]但不知道怎么得出来的,求详解,最好用word写答案后截图下来,不然看不太懂,
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求导:(1)y=(sinx^n)*(cosnx) (2)y=arctan(1/2tanx/2)
(1)n(sinx^n-1)cos(n+1)x
(2)1/[1+3cos(x/2)^2]
但不知道怎么得出来的,求详解,最好用word写答案后截图下来,不然看不太懂,
y=(sinx^n)*(cosnx)
y'=[(sinx)^n]'cosnx +(sinx)^n*(cosnx)'
=cosx*n(sinx)^(n-1)*cosnx +(sinx)^n*n*(-sinnx)
=n*(sinx)^(n-1) *[ cosx*cosnx-sinxsinnx]
=n(sinx)^(n-1)* cos(x+nx)
y=arctan[(tan(x/2))/2]
y'=[tan(x/2)/2]' * [1/[1+(tan(x/2)/2)^2]
=(1/2)*(1/2)*[1/(cos(x/2))^2] * 4/[4+(tan(x/2))^2]
=1/[(cosx/2)^2*(4+(tan(x/2))^2)]
=1/[4(cosx/2)^2+(sin(x/2))^2]
=1/(1+3(cos(x/2))^2)
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