Funções trigonométricas possuem um papel importante e diversas aplicações na nossa vida. A sua periodicidade torna essas funções muito interessantes para descrever certos fenômenos que acontecem com regularidade. Seja n um número natural e f left parenthesis x right parenthesis equals s e n to the power of n left parenthesis x right parenthesis plus s e n left parenthesis x to the power of n right parenthesis. Assinale a alternativa que apresenta f'(x) a. n cos to the power of n minus 1 end exponent left parenthesis x right parenthesis s e n left parenthesis x right parenthesis plus n cos left parenthesis x to the power of n right parenthesis x to the power of n minus 1 end exponent b. n s e n to the power of n minus 1 end exponent left parenthesis x right parenthesis cos left parenthesis x right parenthesis plus n cos left parenthesis x right parenthesis x to the power of n minus 1 end exponent c. n s e n to the power of n minus 1 end exponent left parenthesis x right parenthesis cos left parenthesis x to the power of n right parenthesis plus n cos left parenthesis x to the power of n right parenthesis x to the power of n minus 1 end exponent d. n s e n left parenthesis x right parenthesis cos left parenthesis x right parenthesis plus n cos left parenthesis x to the power of n right parenthesis x to the power of n minus 1 end exponent e. n s e n to the power of n minus 1 end exponent left parenthesis x right parenthesis cos left parenthesis x right parenthesis plus n cos left parenthesis x to the power of n right parenthesis x to the power of n minus 1 end exponent