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# C3 Differentiation Urgent Help watch

1. 1. Find the coordinates of the point where the normal meets the x-axis, given that the equation of the normal = y + e^2x = 1/e^2 (correct answer to previous question

2. If y = e^x - e^-x show that (dy/dx)^2 = y^2 + 4 (!?!?!?!)

Thanks, will rep anyone who helps
2. (Original post by TheKevinFang)
1. Find the coordinates of the point where the normal meets the x-axis, given that the equation of the normal = y + e^2x = 1/e^2 (correct answer to previous question

2. If y = e^x - e^-x show that (dy/dx)^2 = y^2 + 4 (!?!?!?!)

Thanks, will rep anyone who helps
(1) The x-axis is the line y = 0, so set y = 0 in that equation and solve.

(2) if y = e^x - e^-x, then (dy/dx) is e^x + e^-x - the rest is just an algebraic crunch. Do you know about the hyperolic functions Sinh & Cosh? If you do, then notice that
e^x - e^-x = 2 Sinh(x) and use well-known formulae...
3. (Original post by Gregorius)
(1) The x-axis is the line y = 0, so set y = 0 in that equation and solve.

(2) if y = e^x - e^-x, then (dy/dx) is e^x + e^-x - the rest is just an algebraic crunch. Do you know about the hyperolicfunctions Sinh & Cosh? If you do, then notice that
e^x - e^-x = 2 Sinh(x) and use well-known formulae...
New functions?
4. Moved to maths.
5. (Original post by B_9710)
New functions?
If they don't exist, we ought to invent them!
6. (Original post by Gregorius)
(1) The x-axis is the line y = 0, so set y = 0 in that equation and solve.

(2) if y = e^x - e^-x, then (dy/dx) is e^x + e^-x - the rest is just an algebraic crunch. Do you know about the hyperolic functions Sinh & Cosh? If you do, then notice that
e^x - e^-x = 2 Sinh(x) and use well-known formulae...
Thank you. For the first question I misread the answer, but thanks for the help on the second question - much appreciated.

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