一个关于积分上限求导公式的疑问令F(x)=∫(0,x) (x^2-t^2)dt 式1下面对其求导:如果先把F(x)积出来,有F(x)=x^3-x^3/3+C=(2x^3)/3+C,再对x求导有F'(x)=2x^2但是如果直接对式1用积分上限求导公式有(
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![一个关于积分上限求导公式的疑问令F(x)=∫(0,x) (x^2-t^2)dt 式1下面对其求导:如果先把F(x)积出来,有F(x)=x^3-x^3/3+C=(2x^3)/3+C,再对x求导有F'(x)=2x^2但是如果直接对式1用积分上限求导公式有(](/uploads/image/z/5532988-4-8.jpg?t=%E4%B8%80%E4%B8%AA%E5%85%B3%E4%BA%8E%E7%A7%AF%E5%88%86%E4%B8%8A%E9%99%90%E6%B1%82%E5%AF%BC%E5%85%AC%E5%BC%8F%E7%9A%84%E7%96%91%E9%97%AE%E4%BB%A4F%28x%29%3D%E2%88%AB%280%2Cx%29+%28x%5E2-t%5E2%29dt+%E5%BC%8F1%E4%B8%8B%E9%9D%A2%E5%AF%B9%E5%85%B6%E6%B1%82%E5%AF%BC%EF%BC%9A%E5%A6%82%E6%9E%9C%E5%85%88%E6%8A%8AF%EF%BC%88x%EF%BC%89%E7%A7%AF%E5%87%BA%E6%9D%A5%2C%E6%9C%89F%EF%BC%88x%EF%BC%89%3Dx%5E3-x%5E3%2F3%2BC%3D%282x%5E3%29%2F3%2BC%2C%E5%86%8D%E5%AF%B9x%E6%B1%82%E5%AF%BC%E6%9C%89F%27%28x%29%3D2x%5E2%E4%BD%86%E6%98%AF%E5%A6%82%E6%9E%9C%E7%9B%B4%E6%8E%A5%E5%AF%B9%E5%BC%8F1%E7%94%A8%E7%A7%AF%E5%88%86%E4%B8%8A%E9%99%90%E6%B1%82%E5%AF%BC%E5%85%AC%E5%BC%8F%E6%9C%89%EF%BC%88)
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