Question

高等数学，第1题的(1)(2)(3)(4)(5)怎么做，需要详细过程，急急急，求高手

Answer 1

1(1) . z = x^2y -xy^2 = xy(x-y) = (1/2)u^3 sin2v(cosv-sinv)
z'<u> = (3/2)u^2 sin2v(cosv-sinv)
z'<v> = (1/2)u^3 [2cos2v(cosv-sinv)+sin2v(sinv+cosv)]
(2) dz/dt = z'<x>x'<t> + z'<y>y'<t>
= e^(x-2y)cost -2e^(x-2y) 3t^2 = e^(x-2y)(cost - 6t^2)
= e^(sint-2t^3)(cost - 6t^2)
(3) du/dt = u'<x>x'<t>+u'<y>y/<t>+u'<z>z'<t>
= 2xe^t(cost-sint) + 2ye^t(sint+cost) + 2ze^t
= 2e^(2t)cost(cost-sint)+ 2e^(2t)sint(sint+cost) + 2e^(2t)
(4) z = (2x+1)^2 x^9 (3x-1) = 12x^12 + 8x^11 - x^10 - x^9,
dz/dx = 144x^11 + 88x^10 -10x^9 - 9x^8
(5) z'<u> = 2xx'<u> + 2yy'<u> - sin(x+y)(x'<u>+y'<u>)
= 2x - sin(x+y) = 2(u+v) - sin(u+v+e^v)
z'<v> = 2xx'<v> + 2yy'<v> - sin(x+y)(x'<v>+y'<v>)
= 2x + 2ye^v - sin(x+y)(1+e^v)
= 2(u+v) + 2e^(2v) - sin(u+v+e^v)(1+e^v)

追问

第(3)(5)小题怎么弄，可以手写下吗

我们是用这种形式表示的

追答