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

Calculate the amplitude of trigonometry function, Consider the trigonometri...

Consider the trigonometric function f(t) = -3 + 4 cos(Π/ 3 (t - 3/2 )). (a) What is the amplitude of f (t)? (b) What is the period of f(t)? (c) What are the maximum and mi

Some important issue of graph, Some important issue of graph Before mov...

Some important issue of graph Before moving on to the next example, there are some important things to note. Firstly, in almost all problems a graph is pretty much needed.

Trigonometry, Ashow that sec^2x+cosec^2x cannot be less than 4

Ashow that sec^2x+cosec^2x cannot be less than 4

Andrew is helping his mom remodel his room, The perimeter of Andrew''s rect...

The perimeter of Andrew''s rectangular room is 44 feet. What equation was used to find the perimeter?

Sample space, Sample Space is the totality of all possible out...

Sample Space is the totality of all possible outcomes of an experiment. Hence if the experiment was inspecting a light bulb, the only possible outcomes

Algorithm for division, Also, their inability to apply the algorithm for di...

Also, their inability to apply the algorithm for division becomes quite evident. The reason for these difficulties may be many. We have listed some of them below. 1) There are n

Add or subtract operations for complex numbers, performs the mentioned oper...

performs the mentioned operation and write the answers in standard form. ( -4 + 7 i ) + (5 -10 i ) Solution Actually there isn't much to do here other than add or subt

Estimate the probability - noncritical path , An advertising project manage...

An advertising project manager developed the network diagram shown below for a new advertising campagign.  In addition, the manager gathered the time information for each activity,

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