derivative of the function y= (2x+1)^3(x^2+1)

Question

i need this to further understand my lesson last meeting 'cause i'm absent.

Answer 1

y = (2x+1)^3(x^2+1)

Apply derivative to each sides with respect of x.

dy/dx = d/dx[(2x+1)^3(x^2+1)]

= (2x+1)^3 2x+(x^2+1)3(2x+1)^2.2

= (2x+1)^3 2x+(x^2+1)6(2x+1)^2

=(2x+1)^3 2x+6(x^2+1)(4x^2+1+4x)

= (8x^3+1+12x^2+6x)+(6x^2+6)(4x^2+1+4x)

= 8x^3+1+12x^2+6x+24x^4+6x^2+24x^3+24x^2+6+24x

= 24x^4+32x^3+42x^2+30x+7