Differentiate product rule functions, Mathematics

Assignment Help:

Differentiate following functions.

1348_product rules.png

Solution

At this point there in fact isn't a lot of cause to use the product rule. 

We will utilize the product rule.  As we add up more functions to our repertoire and as the functions become more complexes the product rule will become more useful and in several cases required.

Note as well that we took the derivative of this function in the previous section and didn't use the product rule at that point.  However, we have to get the same result here as we did then.

By converting the radical to a fractional exponent as always, we get.

                                                y = x 2/3 (2 x - x2 )

Now let's take the derivative.  Hence we take the derivative of the first function times the second then add up on to that the first function times the derivative of the second function.

                                         y′ = (2/3) x -1/3 (2 x - x2 ) + x 2/3 ( 2 - 2 x )

                          y′ =(4/3)x(2/3)-(2/3) x(5/3) +2x (2/3) -2x (5/3) =(10/3) x(2/3) -(8/3)x(5/3)


Related Discussions:- Differentiate product rule functions

What is the conditional probability based on die questions, A die is rolled...

A die is rolled twice and the sum of the numbers appearing on them is observed to be 7.What is the conditional probability that the number 2 has appeared at least once? A) 1/3

Show frequency tables, Q. Show Frequency Tables? Ans. A frequency ...

Q. Show Frequency Tables? Ans. A frequency table is used to show how often a piece of data occurs. Example: Michelle decides to keep track of the number of phone call

Naming fractions greater than 1, the 10 miles assigned to the chess club st...

the 10 miles assigned to the chess club start at the 10 mile point and go to the 20 mile point when the chess club members have cleaned 5/8 of their 10 mile section between which m

., round 64 to the nearest 10

round 64 to the nearest 10

Draw the digraph for the partial order, 1. Consider the relation on A = {1,...

1. Consider the relation on A = {1, 2, 3, 4} with relation matrix: Assume that the rows and columns of the matrix refer to the elements of A in the order 1, 2, 3, 4. (a)

Geometry help, A painter leans a 10-foot ladder against the house she is to...

A painter leans a 10-foot ladder against the house she is to paint. The foot of the ladder is 3 feet from the house. How far above the ground does the ladder touch the house? Appro

Rate -categories of multiplication, Rate - when we know how many objects...

Rate - when we know how many objects are in a set, and need to find out the total number in several copies of that set. (e.g., if a child uses 4 copybooks in a year, how many co

Student, What is the slope and y intercept for (6,5) (-3,8)

What is the slope and y intercept for (6,5) (-3,8)

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