设z=f(t2,sint),其中f二阶连续可偏导,则d2z/dt2=________.

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问题 设z=f(t2,sint),其中f二阶连续可偏导,则d2z/dt2=________.

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答案2f’1-sint·f’2+4t2f"11+4tcost·f"12+cos2t·f"22

解析 dz/dt=2tf’1+cost·f’2,d2z/dt2=2f’1+2t(2tf"11+cost·f"12)-sint·f’2+cost·(2tf"21+cost·f"22)=2f’1-sint·f’2+4t2f"11+4tcost·f"12+cos2t·f"22
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