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Math Help - Differential Equations

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    Differential Equations

    Please refer to the diagram provided. I don't get the boxed step. I thought when you differentiate, you add to "1". For that question, shouldn't it be \frac{9}{10}(9 - x)^{\frac{10}{9}} ?
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    Quote Originally Posted by Macleef View Post
    Please refer to the diagram provided. I don't get the boxed step. I thought when you differentiate, you add to "1". For that question, shouldn't it be \frac{9}{10}(9 - x)^{\frac{10}{9}} ?
    it's in error, and note the antiderivative also has a negative sign ...

    \int (9-x)^{\frac{1}{9}} \, dx = -\frac{9}{10}(9-x)^{\frac{10}{9}} + C
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