dy/dxif y = 4x3 + 3x2 + 2

The function is 

                                [tex]\displaystyle{ y=4x^3+3x^2+2[/tex].

We recall that the derivative of each monomial [tex]ax^b[/tex] is [tex]a\cdot b\cdot x^{b-1}[/tex], and the derivative of a constant (function) is 0.

According to this:

[tex] \frac{d}{dx}(4x^3+3x^2+2)=4\cdot 3\cdot x^2 + 3\cdot 2\cdot x+0 =12x^2+6x[/tex].


Answer: [tex]12x^2+6x[/tex]