math (1105) - Calc: function of a function

went over something else first.. just revision but into differentiation.

square root x is like x ^ 1/2 basically.. so cube root is x ^ 1/3 etc. and of course x ^ -2 equals x/2

so yeah.. went by that with differentiation.

then.. we learned somehting new.. function of a function.. which was easier than i thought it would be. its for big powers. eg..

differentiate: (x+7)^9

you let u = the number, and y equal u to the pwoer of crap.. observe:

let u = x+7

(du)/(dx) (x+7)
= 1

let y = u^9

(dy)/(du) (u^9)
= 9u^8

then you multiply together.. and the two du cancel each other out.

(dy)/(dx) (1 x 9u^8)
= 9u^8

then you sub in the value of u that we let it equal coz it has to be x

so its 9(x+7)^8

so there ^^