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Prove that (d^n)/(dx^n)(e^(2x)+e^(-2x))=...

Prove that `(d^n)/(dx^n)(e^(2x)+e^(-2x))=2^n[e^(2x)+(-1)^n e^(-2x)]`

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To prove that \[ \frac{d^n}{dx^n}(e^{2x} + e^{-2x}) = 2^n \left[ e^{2x} + (-1)^n e^{-2x} \right], \] we will differentiate the function \(y = e^{2x} + e^{-2x}\) multiple times and look for a pattern. ...
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