Multiplicate a number per an elevated parenthesis I have a little problem in calculating the second derivative of a function, because I don't know how to compute this operation:
$(2x)*(x+2)^2$
I have to calculate the $(x+2)^2$ in this way: $(x^2+4+4x)$ and then multiply every term per $(2x)$ or there is another and faster way?
Thanks

Use the product rule $(fg)' = f'g + g'f$ with $f = 2x$ and $g = (x+2)^2$ so you get $$(2x(x+2)^2)' = (2x)'(x+2)^2 + ((x+2)^2)'(2x)$$
giving $$2(x+2)^2 + 4x(x+2) = 2(x+2)(x+2+2x) = 2(x+2)(3x+2)$$ and then differentiating again with the product rule with $f = x+2$ and  $g = 3x+2$ gives the derivative of $(x+2)(3x+2)$ as $$(x+2)'(3x+2) + (3x+2)'(x+2) = 3x+2+3(x+2)$$ 
and accounting for the factor of $2$ gives you what you want: $4(3x+4)$
