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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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`(d)/(dx)[e^(2x)+e^(-2x)]=2e^(2x)-2e^(-2x)=2^(1)[e^(2x)-e^(-2x)]`
`(d)/(dx^(2))(e^(2x)+e^(-2x))=(d)/(dx)(e^(2x)-e^(-2x))=2^(2)(e^(2x)+e^(-2x))`
`(d^(3))/(dx^(3))(e^(2x)-e^(-2x))=(d)/(dx)2^(2)(e^(2x)+e^(-2x))=2^(3)(e^(2x)-e^(-2x))`
`because" "(d^(n))/(dx^(n))[e^(2x)+e^(-2x)]=2^(n)[e^(2x)+(-1)^(n)e^(-2x)]`
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