16.09.2019
$$f(x) = {{{e^x} + {e^{ - x}}} \over 2} \to {D_f} = \mathbb{R} $$ $$f'(x) = {{{e^x} - {e^{ - x}}} \over 2} $$ $$f''(x) = {{{e^x} + {e^{ - x}}} \over 2} = f(x)$$ $$f'''(x) = f'(x)$$Erinnerung:
$$f(x) = sin(x)$$ $$f''''(x) = sin(x)$$ $${f^{(4)}}(x) = f(x)$$ $${f^{4}}(x) = f(f(f(f(x))))$$ $${f^{4}}(x) = f \circ f \circ f \circ f(x)$$ $${f^{4}}(x) = (sin(x))^{4} = sin(x)^{4}$$