I think the formula used abouve for delta P is wrong.

F = P * A

dF/F = dP/P + dA/A

dP/P = dF/F - dA/A

I see a similar mistake in another site too. Please validate.

F = P * A

dF/F = dP/P + dA/A

dP/P = dF/F - dA/A

I see a similar mistake in another site too. Please validate.