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设Φ(x)=∫_x^x²e^tdt，求Φ′(x)．

高老师2年前 (2024-03-27)高等数学（工专）(00022)10

设Φ(x)=∫_x^x²e^tdt，求Φ′(x)．

Φ′=(d/dx)∫_x^x²e^tdt=d/dx[∫₀^x²e^tdt-∫₀^xe^tdt] =e^x²(x²)-e^x=2xe^x²-e^x

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