Question

what is the derivative of: (4x)^3 * (2x)^6 ?

Answer 1

y = [(4x)^3]*[(2x)^6]

The Product Rule: d(f•g)/dx = f´g + fg´

y´ = [(4x)^3]*(6)(2x)^5 (2) + [(2x)^6]*(3)(4x)^2 (4)

y´ = 12[(4x)^3]*[(2x)^5] + 12[(4x)^2]*[(2x)^6]

Factor out a 4x from one term and a 2x from the other in order to add them together...

y´ = 12(4x)[(4x)^2]*[(2x)^5] + 12(2x)[(4x)^2]*[(2x)^5]

y´ = [48x + 24x]*[(4x)^3]*[(2x)^5]

y´ = (72x)*[(4x)^3]*[(2x)^5]

Answer 2

thank you1 :D

Answer 3

No Problem =D