Question

If y = x3 + 3x2 + 5, what is dy/dx A. 3x2 + 6x + 5 B. 6x2 C. 6x2 D. 3x2 + 6x 

Answer 1

You have to use these facts:

1) The derivative of a sum is the sum of the derivatives

2) d[x^n] / dx = n x ^ (n - 1)

3) d [a(f(x) ] / dx = a d [f(x)] / dx

=> d [x^3 + 3x^2 + 5] / dx =  d[x^3]/dx + 3d[x^2]/dx + 0

= 3x^2 + 6x

Answer: option D. 3x^2 + 6x