Question

Sendo f(x) = x³ * e (elevado a 3x) determine a determinada segunda f''(x)

Answer 1

Resposta:

f(x) = x³ * e (elevado a 3x)

f(x) =x³ *e^(3x)

Regra do produto

f'(x) = (x³)' * e^(3x) +x³ * (e^(3x)'

*******(e^(3x)' =(3x)' * (e^(3x) =3 * (e^(3x)

f'(x) =3x² * e^(3x) +x³ * 3 * e^(3x)

f''(x)= (3x²)' * e^(3x)  +3x² * (e^(3x))'  + 3 * (x³)'*e^(3x) +3 *x³ * (e^(3x))'

f''(x)= (6x) * e^(3x)  +3x² * 3*e^(3x)  +9 * x² * e^(3x) +3 *x³ * (3*e^(3x))

f''(x)= 6x * e^(3x)  +9 *x² *e^(3x)  + 9 * x² * e^(3x) +9 *x³ * e^(3x)

f''(x)= 6x * e^(3x)  +18*x² *e^(3x)   + 9 *x³ * e^(3x)

f''(x)= 3x * e^(3x)  * [2  +6*x   + 3*x² ]