Introduction to the Chain Rule of Differentiation
This video introduces the chain rule of differentiation.
Transcript
00:01Welcome to an introduction
00:02to the chain Rule of differentiation.
00:04The chain rule is a differentiation
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00:18of the outer function evaluator
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undefined:undefinedof X of the spect X is equal
00:36to F prime of G of X times
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undefined:undefinedrule using ness notation,
00:54where if U is the inner
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01:12I think an easy way to
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undefined:undefinedwhere once again F prime
01:32of U is a derivative
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undefined:undefinedfunction is two x plus one and
01:47therefore we let U equal two x plus one.
01:49Let's go ahead and find U prime.
01:51Now U prime
01:52or DUDX is equal to two,
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undefined:undefinedwhere F prime of U is equal
02:08to three U squared giving us F prime
02:12of X equals three U square times U prime.
02:14From here we replace U
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undefined:undefinedI have the general power rule
02:44or the power rule that
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undefined:undefinedinner function and label it U.
03:04Notice here we have U
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undefined:undefinedthe chain rule is equal
03:23to F prime of U times U prime.
03:26F prime of U is a derivative
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undefined:undefined12 x squared is equal
03:51to 168 x squared giving us F prime
03:54of X equals 168 x squared
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undefined:undefinedG prime of X equals G prime
04:31of U times U prime, where G prime of U
04:35is at derivative of five.
04:37You to the one half with the spec to U,
04:39which is five times one
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undefined:undefinedsquared plus five x minus two
04:54and you prime with four x plus five
04:56and simplify performing
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undefined:undefinedLet's write this as G.
05:10Prime of x equals five halves times
05:13the quantity four x plus
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05:28And finally, we can also
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05:50to the exponent of three
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undefined:undefinedprime of U is 11 E to the U.
06:09And then again, we have times U prime
06:11performing substitutions for U
06:13and U prime, we have H pima X
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undefined:undefinedh PIM of X equals 264 x
06:29of the seventh E of the power
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undefined:undefinedx squared minus eight x.
06:50We can now write G as a function of U as G
06:52of U equals four natural log
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undefined:undefinedequals the product of four
07:21and three x squared minus eight.
07:24I'll divide it by the quantity
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