# Math Help - Differential Equations

1. ## 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 $\frac{9}{10}(9 - x)^{\frac{10}{9}}$ ?

2. Originally Posted by Macleef
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 ...

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