Monday, April 20, 2015

blog 4


Hello students today I will explain the chain rule

The chain rule is a formula for computing the derivative of the composition of two functions. That is, if f and g are functions, then the chain rule expresses the derivative of their composition written with a different notation for function composition as follows:

d/dx (f (g (t)) = f ’ ( g(t) ) * g’ (t)

The chain rule may be written, in Leibniz's notation, in the following way:

dz/dx = dz/dy * dy/dx

Examples:

A)   Y= (4t² + 1)³

Y ΚΌ= 3(4t² + 1)² * (8t)

 

B)    X = (3t³ - t)³

X’= 3(3t³ - t) ² * (9t² -1)

 

C)    G = 5 Ln (2t² +3)

G’ = 5 * 1/2t² +3 * 4t

     = 20t/2t² +3

 

The purpose of the chain rule is to find the derivative of a composite function, and to simplify a complicated derivative into several easier derivatives.  

5 comments:

  1. The examples were helpful to see how you solved! Easy to follow.

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  2. Your blog is clean and well organized. It's a little short, but I think you covered the concept well.

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  3. these examples were nicely put together and very organized. well done

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  4. sara,

    nice explanation of how to do the chain rule. your examples were good, but it would have been nice to see a little bit more or of a step by step explanation for each problem. generally, good job, though.

    professor little

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  5. Nice examples. very organized. well done

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