Find the first derivative of 2x^3+5x^2+4x+1 (with respect to x)

In differentiation, your goal is to reduce the power of the terms that you're differentiating with respect to (in this case, x).The method for doing this is:Multiply the power of your x term by its coefficient;Reduce the power of the x term by 1.This is done term-by-term. So the first derivative of a(x^b) would become ab(x^(b-1)).With our example, the first term is 2x^3. Multiply the 3 by the 2, giving 6x^3, then reduce the power by 1, giving 6x^2. Follow the same process with 5x^2, giving 10x.To differentiate 4x, you can consider 4x as 4x^1. So then 4*1=4 for the coefficient, then 1-1=0 for the power, so the first derivative of 4x is 4x^0, or 4 (as x^0=1).Finally, to differentiate a constant, 1 in this case, you realise that there is no x term attached to this number. So when differentiating the term, i.e. reducing the powers of x, there is nothing to reduce, so this number becomes 0.Putting this all together, the first derivative of 2x^3+5x^2+4x+1, with respect to x, is 6x^2+10x+4.