# Explanation of Chain Rule

Please explain chain rule

i'm a visual person please show several examples

© BrainMass Inc. brainmass.com October 16, 2018, 6:49 pm ad1c9bdddfhttps://brainmass.com/math/derivatives/explanation-chain-rule-95835

#### Solution Preview

Hello and thank you for posting your question to Brainmass!

The solution is attached below in two files. the files are identical in ...

#### Solution Summary

This solution is comprised of a detailed explanation to explain chain rule.

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.

(give answer in explicit form.)