Differentiate from first principles, with respect to x, (3x(^2) + 2x – 1)
Explanation
Substitute x by (x + h) to have f(x + h) = 3(x + h)(^2) + 2x + 2h – 1 – 3x(^2) – 2x + 1
= 6(x)h + 3h(^2) + 2h
Divided through by h and obtained (frac{f(x + h) – f(x)}{h} = frac{6 times h + 3h^2 + 2h}{h} = 6x + 3h + 2)
Taking limit as h tends to zero, lim(_{h to o}) (frac{f(x+h) -f(x)}{h})
= lim(_{h to o}) (6x + 3h + 2) so that f(^1)(x) = 6x + 2