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.
The examples were helpful to see how you solved! Easy to follow.
ReplyDeleteYour blog is clean and well organized. It's a little short, but I think you covered the concept well.
ReplyDeletethese examples were nicely put together and very organized. well done
ReplyDeletesara,
ReplyDeletenice 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
Nice examples. very organized. well done
ReplyDelete