请求数学高手求助!!大学经济数学
求由方程2x^2+e^(xy)-y^2=0所确定的函数的导数dy/dx
4x +[y +x(dy/dx)] e^(xy) -2y (dy/dx) =0
[2y -xe^(xy)](dy/dx) = 4x + ye^(xy)
(dy/dx) = [4x + ye^(xy)]/[2y -xe^(xy)]
设函数f(x)=x^3-3x^2-24x-2求其在【-5,5】的最大值,最小值及单调区间
f'(x)= 3x^2-6x -24 =3(x +2)(x -4)= 0
x1 =-2 , x2 = 4
∵f(-5)=-82,f(4)=-82
∴f(x)在[-5,5]的最小值是-82;
∵f(-2)=...全部
求由方程2x^2+e^(xy)-y^2=0所确定的函数的导数dy/dx
4x +[y +x(dy/dx)] e^(xy) -2y (dy/dx) =0
[2y -xe^(xy)](dy/dx) = 4x + ye^(xy)
(dy/dx) = [4x + ye^(xy)]/[2y -xe^(xy)]
设函数f(x)=x^3-3x^2-24x-2求其在【-5,5】的最大值,最小值及单调区间
f'(x)= 3x^2-6x -24 =3(x +2)(x -4)= 0
x1 =-2 , x2 = 4
∵f(-5)=-82,f(4)=-82
∴f(x)在[-5,5]的最小值是-82;
∵f(-2)=24,f(5)=-72
∴f(x)在[-5,5]的最大值是24;
单调增区间:[-5,-2],[4,5]
单调减区间:[-2,4]
设函数y^2+lnxy=sin2x,求dy
2y(dy) +[1/(xy)][y(dx) +x(dy)] = [2cos(2x)](dx)
[2y + 1/y](dy) = [2cos(2x) -1/x](dx)
dy ={[2cos(2x) -1/x]/[2y + 1/y]}(dx)
设函数y=cos^3x-[(x-1)/√x]求dy
y = (cosx)^3 + 1/(√x) -√x
dy =3[(cosx)^2](-sinx)(dx)-(1/2)[x^(-3/2)](dx)-(1/2)[x^(-1/2)] (dx)
=-{3sinx(cosx)^2 +[x^(-3/2)]/2 +[x^(-1/2)]/2}(dx)。
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