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# Explanation of Chain Rule

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i'm a visual person please show several examples

https://brainmass.com/math/derivatives/explanation-chain-rule-95835

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## Quotient and Composite Rules

1.
a. use quotient rule to find derivative of this function. f(x) = (20+16x-x^2)/(4+x^2).
b. Find any stationary points of the function from 1a. An use the first derivative test to see whether they are local maximum or local minimum of f(x).
c. what are the maximum and minimum values of the function f(x) at interval [-6,2]

2.
a. differentiate the following using composite rule: g(x)=sqrt(1+x^2)
b. use the answer from 2a and composite rule to find the derivative of: k(x)=ln(x+sqrt[1+x^2])

c. using answer 2b, solve the initial value problem:

dy/dx =y/(sqrt[1x^2]) (y>0) y=2 when x=0.