This week was INTENSE!!!!!!!!!!!! Nah not really, but we did leard how to do the chain rule and for the most part it seems pretty easy. The formula for d / dx f (g ( x ) ) = f' (g ( x ) ) X g'( x ) or in words, which is a lotttttt easier to understand, ( derivative of outside ) ( plug in the inside ) times ( the derivative of the inside ). U stands for the inside of the problem and Y is the problem. Before you plug into the formula you first have to break down the problem and get the inside and outside.
Ex :
( cos x ) ^2
u= cos x
y= ( u ) ^2
-derivative of outside = 2( u )
-plug in inside = 2( cos x )
-multiply by derivative of inside = 2( cos x ) ( -sinx )
-your answer is 2cosx( -sinx )
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