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# Integrating sec x dy/dx = e^y watch

1. I just wanted to check this, I'm trying to get the general solution:

I separate the variables to get

because of the rule that

So

The answer I have on the sheet is
why is the e minus?

thanks!
2. You've separated the variables correctly. If you think about it:

if y = e^f(x)
then dy/dx = f'(x)e^f(x).

Try differentiating e^-y and -e^-y.

The first will give you -e^-y (dy/dx) and the latter will give you e^-y (dy/dx)
3. integral of e^(-y) is -e^(-y).
Since integral of e^(ax+b) is (1/a)*e^(ax+b)
4. As you may well imagine, it's a really simple error:

when you integrate e^-y with respect to y, you get -e^-y, because of the chain rule. The derivative of -y is -1, which multiples with e^-y to give -e^-y.
5. (Original post by mh1985)
So
This bit is wrong.

In general, for linear powers, we know that:

Where and are constants, and

Remember that this won't work in general, it has to be in the form I've highlight above for this exact 'rule' to follow.
6. Thanks a lot everyone! Will rep when on recharge

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