find the derivative of 3x^2(x+2)^4?

Question

please provide answer and detail

Answer 1

First you need to understand the derivitives of products
if f(x) = f'x * f''x then df/dx = f'x * df''x/dx + f''x * df'x/dx
so your function becomes
3x^2 * d/dx (x+2)^4 + (x+2)^4 * d/dx (3x^2)
equals
3x^2 * 4(x+2)^3 + (x+2)^4 * 6x
and taking out the common factors 6x and (x+2)^3
2x * 6x(x+2)^3 + (x+2) * 6x(x+2)^3
equals
6x(3x+2)(x+2)^3

Answer 2

3x^2(x+2)^4
(x+2)^4=x^4+16x+16
3x^2(x^4+16x+16)=3x^6+48x^3+48x^2
(6x3)=18, 48x3=144, 2x48=96
answer:18x5+144x2+96x
Hope that helps!!!