Differentiation of composite function really need help

Find the dy/dx for y=x^2(x+2)^4



First I want to show you my calculation :

Let u = x^2, so du/dx = 2x

Let v = (x+2)^4, so dv/dx = 4(x+2)^3

dy/dx = x^2 [4(x+2)^3] + (x+2)^4 (2x)

= 4x^2 (x+2)^3 + 2x (x+2)^4



Okay, so the answer is 2x(x+2)^3(3x+2)




How can I get 2x(x+2)^3(3x+2) from 4x^2 (x+2)^3 + 2x (x+2)^4 ?

Explain please, so that I can solve this question ! Thanks. :)

you can just apply product rule here...

y=x^2(x+2)^4

take derv of first term multiplied by second term

2x(x+2)^4

then add the derv of second term multiplied by first term

2x(x+2)^4 + 4x^2(x+2)^3

Then factor out the (x+2)^3 from both and group what remains.

(x+2)^3 (2x(x+2) + 4x^2))

simplify

(x+2)^3 (2x^2 + 4x + 4x^2)

(x+2)^3 (6x^2 + 4x)

then factor out 2x WITHIN THE SECOND TERM ALONE.

(x+2)^3 * 2x * (3x^2 + 2x)

leaving

2x(3x + 2)(x+2)^3

4x^2 (x+2)^3 + 2x (x+2)^4 = 2x(x+2)^3 [2x + x + 2] = 2x(x+2)^3(3x+2)
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Ideas: GCF = 2x(x+2)^3