bila f(x)=2xpangkat3-3xpangkat2+x-10 maka f'(x)=

f(x) = 2x^3 – 3x^2 + x – 10

f(x+h) = 2(x^3 + x^2 h + 2x^2 h + 2xh^2 + xh^2 + h^3) – 3(x^2 + 2xh + h^2) + (x + h) – 10

= 2x^3 + 2x^2 h + 4x^2 h + 4xh^2 + 2xh^2 + 2h^3  - (3x^2 + 6xh + 3h^2) + (x + h) – 10

= 2x^3 + 2x^2 h + 4x^2 h + 4xh^2 + 2xh^2 + 2h^3  - 3x^2 - 6xh - 3h^2 + x + h – 10

F’(x) = lim(h>0)  f(x+h) - f(x) / h

 = lim(h>0)  (2x^3 + 2x^2 h + 4x^2 h + 4xh^2 + 2xh^2 + 2h^3  - 3x^2 - 6xh -     3h^2 + x + h – 10) – (2x^3 –  3x^2 + x – 10) / h

 = lim(h>0)  2x^3 + 2x^2 h + 4x^2 h + 4xh^2 + 2xh^2 + 2h^3  - 3x^2 - 6xh - 3h^2 + x + h  – 10 – 2x^3 +  3x^2  - x + 10 / h

= lim(h>0) 2x^2 h + 4x^2 h + 4xh^2 + 2xh^2 + 2h^3  - 6xh - 3h^2  + h / h         (selanjutnya pisahkan h nya)

= lim(h>0) h(2x^2 + 4x^2 + 4xh + 2xh + 2h^2 - 6x - 3h + 1) / h  (h dan h di     coret)

= lim(h>0) 2x^2 + 4x^2 + 4xh + 2xh + 2h^2 - 6x - 3h + 1

= lim(h>0) 6x^2 + 6xh + 2h^2 - 6x – 3h + 1 (lalu subsitusi nilai h = 0)

= lim(h>0) 6x^2 + 6x(0) + 2(0)2 – 6x – 3(0) + 1

= lim(h>0) 6x^2 + 0 + 0 – 6x – 0 + 1

          = 6x^2 – 6x + 1.

Selesai, kalau misalnya salah saya mohon maaf.