Differentiate outline function in chain rules, Mathematics

Assignment Help:

Differentiate following.

1924_outside function.png

Solution :It requires the product rule & each derivative in the product rule will need a chain rule application as well.

T ′ ( x ) =1/1+(2x)2 (2) (1-3x2)(1/3) +tan-1(2x)(1/3)(1-3x2)(-2/3)(-6x)

= 2(1 - 3x2 )(1/3)  /(1+(2x)2 - 2(1 - 3x2 )-(2/3)  tan -1 ( 2x )

We know that,

d (tan -1 x ) / dx =  (1/(1+x2)

While doing the chain rule with this we remember that we've got to leave the inside function

alone. That means that where we have the x2  in the derivative of tan -1 x we will have to have (inside function )2 .


Related Discussions:- Differentiate outline function in chain rules

Equal groupings -categories of multiplication, Equal groupings - when we...

Equal groupings - when we want to find how many objects there are in several equal-sized sets. (e.g., if there are 3 baskets, each with 4 bananas, 4 oranges and 4 apples, respec

Scatter graphs, Scatter Graphs - A scatter graph is a graph that compr...

Scatter Graphs - A scatter graph is a graph that comprises of points which have been plotted but are not joined through line segments - The pattern of the points will defin

Comparison test for improper integrals - integration, Comparison Test for I...

Comparison Test for Improper Integrals Here now that we've seen how to actually calculate improper integrals we should to address one more topic about them.  Frequently we ar

Between that two call numbers should she place the book, A librarian is ret...

A librarian is returning library books to the shelf. She uses the call numbers to denote while the books belong. She requires placing a book about perennials along with a call numb

Rate of change interpretation of derivative, Rate of Change : The first in...

Rate of Change : The first interpretation of derivative is rate of change.  It was not the primary problem which we looked at in the limit chapter, however it is the most signific

Definition of a function, A function is a relation for which each of the va...

A function is a relation for which each of the value from the set the first components of the ordered pairs is related with exactly one value from the set of second components of t

Shares and dividend, A man invests rs.10400 in 6%shares at rs.104 and rs.11...

A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all??

What is this distance expressed in standard notation, The distance from the...

The distance from the sun to the earth is approximately 9.3 × 10 7 miles. What is this distance expressed in standard notation? In order to convert this number to standard not

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd