Second Holiday Reflection

Chain Rule :
you take the derivative of the outside, then derivative of the outside then recopy the inside, multiply by derivative inside.
d/dx f(g(x)) = f'(g(x)) X g'(x)

Examples :

f(t) = (9t+2)^2/3
y = u^2/3 u = 9t+2
2/3u^-1/3 X 9
2/3(9t+2)^-1/3 X 9
6(9t+2)^-1/3
= 6/(9t+2)^-1/3

y = sin(pix)^2
cos(pix)^2 X 2pix
= 2pixcos(pix)^2

Derivative Shortcut :

4x^3 +2x -5
4(3)x^3-1 + 2 – 0
= 12x^2 + 2