Question

derivada de f(x) = (xsen)² .(x−2)

Answer 1

f(x) = x²*sen (x−2)

***Regra do produto   ==> f =u * v    ==> f'= u' * v + u * v'

f'(x) =(x²)' * sen (x-2) + x² * [sen(x-2)]'

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derivada de sen(x-2) ,

***Vou usar a regra da cadeia

f = sen u  ==> f' = u ' * [sen u]'   = u' * cos u

[sen(x-2)]' = (x-2)' * cos(x-2)   = 1 *cos (x-2) =cos (x-2)

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f'(x)= 2x * sen(x-2) + x² * cos (x-2)  é a resposta