百科知识

教育/科学

求下列函数的导数:(1)y=sin^2x+sin2x(2)y=1

2006-12-19 17:42:25a***
(1)y=sin^2x+sin 2x (2)y=1/根号x^2-1 (3)y=x^2根号x+x根号x-1/根号x 希望有完整的解题步骤～谢谢咯！求下列函数的导数:(1)y=sin^2x+sin2x(2)y=1/根号x^2-1(3)y=x^2根号x+x根号x-1/根号x希望有完整的解题步骤～谢谢咯！：1)?

最佳回答

  • 1)y'=[(sinx)^2]'+(sin2x)' =2sinx*(sinx)'+cos2x*(2x)' =2sinxcosx+2cos2x. =sinx+2cos2x 2)y'=[(x^2-1)^(-1/2)]' =-1/2*[(x^2-1)^(-1/2-1]*(x^2-1)' =-x/[(x^2-1)^(3/2)] =x/[(x^2-1)√(x^2-1)] 3)'=[x^(5/2)]'+[x^(3/2)]'-[x^(-1)]' =5/2*[x^(5/2-1)]+3/2*[x^(3/2-1)]-(-1/2)*x^(-1/2-1) =5/2*x^(3/2)+3/2*x^(1/2)+1/2*x^(-3/2) =[5x√x+3√x+1/(x√x)]/2
    2006-12-19 18:25:38
  • （1）y'=2sinx·(sinx)'+cos2x·(2x)' =2sinx·cosx+cosx·2 =sin2x+2cos2x （2）y=(x^2-1)^(-0.5) y'=-0.5*(x^2-1)^(-1.5)*(x^2-1)' =-x*(x^2-1)^(-1.5) (3)y=x^(2.5)+x*(x-1)^0.5-x^(-1) y'=2.5x^1.5+x'*(x-1)^0.5+x*[(x-1)^0.5]'+x^(-2) =2.5x^1.5+(x-1)^0.5+x*[0.5(x-1)^(-0.5)]+x^(-2) =2.5x^1.5+(x-1)^0.5+0.5x(x-1)^(-0.5)+x^(-2)
    2006-12-19 18:18:54
    • 很赞哦！ (152)

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