chain rule

chain rule - The Chain Rule How do we differentiate the...

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The Chain Rule How do we differentiate the function? We could multiply the whole thing out but that would take WAY too long Instead, we notice that there is an “inside part” (inside the bracket) that we can differentiate easily What we are doing to the bracket is the “outside part” We also know how to differentiate this using the power rule something something

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What the chain rule says is that when we have a function with an “inside part” and an “outside part” Chain rule says, to differentiate we must take Derivative of the “outside part” the inside bit doesn’t Change here! Derivative of the inside part the derivative of the outside part multiplied by the derivative of the inside part
Inside part Outside part Derivative of the Outside part

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We can make this more mathematical When we talk about “inside” and “outside” parts we mean having a function inside another function and Then When we sub the function t in we get So the function is inside the function
Try the following examples: (a) (b) (c) Calculate the derivative in each case

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(a) (b) (c)
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