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

Pre Calculus 12, A radioactive substance decays to 30% of its original mass...

A radioactive substance decays to 30% of its original mass in 15 months. Determine the half-life of this radioactive substance to the nearest month

Calculate the time average of kinetic energy of the planet, (1) If the coef...

(1) If the coefficient of friction between a box and the bed of a truck is m , What is the maximum acceleration with which the truck can climb a hill, making an angle q with the ho

Differential equations, solve the differential equation 8yk+2-6yk+1+yk=9 ,k...

solve the differential equation 8yk+2-6yk+1+yk=9 ,k=0 given that Y0=1 and y1=3/2

Sqrt n- sqrt 8836, How many integers satisfy (sqrt n- sqrt 8836)^2 Solutio...

How many integers satisfy (sqrt n- sqrt 8836)^2 Solution) sqrt 8836 = 94 , let sqrt n=x the equation becomes... (x-94)^2 (x-94)^2 - 1 (x-95)(x-93) hence  93 8649  the number o

Tied rankings, Tied Rankings A slight adjustment to the formula is mad...

Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied

Do all our activities involve mathematics?, Do All Our Activities Involve M...

Do All Our Activities Involve Mathematics? :  The answer to this is 'yes' and 'no'. For those who look for mathematics and know where to look for it, it is 'yes'. For those who do

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