∵z=uv，u=e^t，v=cost
∴z=(e^t)cost
∴dz/dt
=[(e^t)cost]/dt
=[(e^t)/dt]cost+[(cost)/dt](e^t)
=(e^t)cost-(e^t)sint
=(e^t)(cost-sint)
=√2(e^t)(√2/2cost-√2/2sint)
=√2(e^t)(cos45°cost-sin45°sint)
=√2(e^t)cos(t+45°)
先到(e^t)(cost-sint)
然后化简。
z=uv
dz/du= v+u(dv/du)
u=e^t
du/dt = e^t
v=cost
dv/dt = -sint
dz/dt = dz/du. du/dt
= (v+ u(dv/dt)) e^t
=(v- usint)e^t
dz/dt
=d(uv)/dt
=u(dv/dt)+v(du/dt)
=-e^t*sint+e^t*cost
=e^t(cost-sint)
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