几道高数题求步骤求答案1）已知y=x^3lnx,则y^n(1)=2）设y=cos2x,则dy=3）若y=2e^x+x^6,则y^（7）=

Question

几道高数题求步骤求答案 1）已知y=x^3lnx,则y^n(1)= 2）设y=cos2x,则dy= 3）若y=2e^x+x^6,则y^（7）=

Answer 1

1）已知y=x^3 lnx,y ' = 3x^2 lnx + x^2
y '' = 6x lnx + x,y ''' = 6 lnx + 1,y '''' = 6/x
y ^ (n) = 6 * (-1)^(n-4) * (n-4)!/ x^(n-3)
y '(1) =1,y ''(1) =1,y '''(1) =1,y ''''(1) = 6,
y^(n) (1) = 6 * (-1)^(n-4) * (n-4)!
2) 设y=cos(2x),dy= y ' dx = -2 sin(2x) dx
3) 若y= 2e^x + x^6,y^(7) = 2 e^x + 0 = 2 e^x