Example:
Find f'(a) for f(x)=3x^4+7x^3-20x-9.
Solution:
By Rules of differentiation we have, ((using the notation ' for derivative))
(1) (3x^4)' = 3(x^4)' = 3(4x^(4-1)) = 12x^3 --> power rule
(2) (7x^3)' = 7(x^3)' = 7(3x^(3-1)) = 21x^2 --> power rule
(3) (-20x)' = -20(x^1)' = -20 --> power rule
(4) (-9)'=0 --> derivative of constant is 0.
Note for (3): If you draw the line y=mx, choose any two points and find the slope between the two chosen points, then you will get that the slope is m. (This is another reason why (mx)'=m.)
Note for (4): Same way (as in note for (3)) you can draw the line y=m, choose any two points on it, and find the slope, you will always get that the slope is 0. (This is another reason why the derivative of constant is 0.)
So, having differentiated each component, you get:
f'(x)=12x^3+21x^2-20.
Then, since you want to find f'(a), plug in x=a into f'(a). That gives you,
f'(a)=12a^3+21a^2-20.