Differentiate 4(x^3) + 3x + 2 with respect to x

Solution: 12x² + 3

Working:

General differentiation formular:  d/dx (axⁿ ) = an(x^n-1) 

So we multiply the coefficient (constant infront) of the x term by the power of x (in this case: n) and reduce the power by 1.

d/dx (4x³ + 3x +2) = d/dx (4x³) + d/dx(3x) + d/dx(2)

                              = 43x^3-1 + 31x^1-1 + 0

                              = 12x² + 3

Note: for the second term in the expression, x can be written x¹ and also x⁰ = 1. This is true for any value to the power of zero.

Notation: 3*4 = 3 times 4 =12