# calculus - derivatives

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can you please find the first 5 derivatives for:

f(x) = (0.5e^x)-(0.5e^-x)

f'(x) = ?
f''(x) = ?
f'''(x) = ?
f''''(x) = ?
f'''''(x) = ?

thanks :)

f(x) = (0.5e^x)-(0.5e^-x)

f'(x) = 0.5 e^x + 0.5 e^-x
f''(x) = 0.5 e^x - 0.5 e^-x
f'''(x) = 0.5 e^x + 0.5 e^-x
f''''(x) = 0.5 e^x - 0.5 e^-x
f'''''(x) = 0.5 e^x + 0.5 e^-x

The first term stays the same; the second term changes sign with each differentiation. The situation is related to the hyperbolic functions sinh x and cosh x

gotcha. thanks

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