Question

calcule a derivada da funções f (X)=(1+X)²e²×

Answer 1

Oi Neo

f(x) = (1 + x)²*e^(2x) = g(x)*h(x)

g(x) = (1 + x)² , g'(x) = 2x + 2
h(x) = e^(2x) ,  h'(x) = 2*e^(2x)

derivada

f'(x) = g(x)*h'(x) + h(x)*g'(x)

f'(x) = (1 + x)²*2*e^(2x) + e^(2x)*(2x + 2)

f'(x) = e^(2x)*(2*(1 + x)² + 2x + 2)

f'(x) = e^2x*(2x² + 4x + 2 + 2x + 2)

f'(x) = e^2x*(2x² + 6x + 4)