To differentiate a simple equation: y= 4x^3 + 7x

y = 4x^3 + 7 x

Recall: to differentiate any function of the form y = x^n

dy/dx = y' = n x^(n-1)

Hence if y = 4x^3 + 7x

dy/dx = 4 ( 3x^3 -1) + 7x^(1-1)          

= 12 x^2 + 7