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Differentiating The Chain Rule

Differentiating The Chain Rule. e.g. 1 Find if. We need to recognise the function as and identify the inner function ( which is u ). Solution:. Let. Then. Differentiating:. We don’t multiply out the brackets.

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Differentiating The Chain Rule

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  1. DifferentiatingThe Chain Rule

  2. e.g. 1 Find if We need to recognise the function as and identify the inner function ( which is u ). Solution: Let Then Differentiating: We don’t multiply out the brackets

  3. The chain rule can also be used to differentiate functions involving e. e.g. Differentiate Solution: The inner function is the 1st operation on x so here it is -2x. Let

  4. Later we will want to reverse the chain rule to integrate some functions of a function. To prepare for this, we need to be able to use the chain rule without writing out all the steps. e.g. For we know that The derivative of the inner function which is has been multiplied by the derivative of the outer function which is ( I’ve put dashes here because we want to ignore the inner function at this stage. We mustn’t differentiate it again. )

  5. So, the chain rule says • differentiate the inner function • multiply by the derivative of the outer function e.g. ( The inner function is ) ( The outer function is ) With exponential functions, the index never changes.

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