Question

Derivada da função(x)= X^4*a^2X

Answer 1

f(x) = x⁴ * a^(2x)

dy/dx =(x⁴)' * a^(2x) + x⁴ * [a^(2x)]'

_______________________________________________

**** y=a^(2x)

****ln y = ln a^(2x)

****ln y =2x * ln a

****y = e^[(2x) * ln a]

***y' = [(2x) * ln a]' * e^[(2x) * ln a] = 2*ln a * e^[(2x) * ln a]

Como y=a^(2x) = e^[(2x) * ln a]

***y' = [(2x) * ln a]' * e^[(2x) * ln a] = 2*ln a * a^(2x)]

_______________________________________________

dy/dx =4x³ * a^(2x) + x⁴ * 2*ln a * a^(2x)]

dy/dx =2x³*a^(2x) * [2 + x *ln a ]