find derivative of f(x) = 2(x^2)(e^4x)?

Question

also f(x) = (x^-4)(ln x^5)

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show steps. thanks

Answer 1

2[x^2*4e^4x+e^4x*2x]
=4xe^4x(2x+1)

Answer 2

derivative of x^2 = 2x ; derivative of e^4x = 4 e^4x

derivative of a product of functions d (uv) = u' v + u v'

so df(x)/dx = 2 (2x e^4x + (x-2) 4 e^4x)) = 2(6x-8)e^4x

Final df(x)/dx = e^4x (12x-16)

Answer 3

f(x)/2 = (x^2)(e^4x)
f'(x)/2 = (x^2)d/dx(e^4x) + (e^4x)d/dx(x^2)
d/dx(e^4x) = 4e^4x
d/dx(x^2) = 2x
f'(x)/2 = (x^2)(4e^4x) + (e^4x)(2x)
f'(x) = 2[4(x^2)e^4x + 2x(e^4x)] = 4x(e^4x)[2x + 1]