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

Seriation to developing pre-number concepts, Seriation :  You have read ab...

Seriation :  You have read about a preschooler's ability to order. Ordering a set of objects means to arrange them in a sequence according to some rule. This arrangement could be

Find out a series solution for differential equation, Find out a series sol...

Find out a series solution for the following differential equation about x 0 = 0 y′′ + y = 0.   Solution Note that in this case p(x)=1 and therefore every point is an or

Differential calculus finding limits, how can i evaluate this lim of x as x...

how can i evaluate this lim of x as x approaches to a

Detemine the amplitude of trigonometric function, 1. Consider the trigonome...

1. Consider the trigonometric function f(t) = (a) What is the amplitude of f(t)? (b) What is the period of f(t)? (c) What are the maximum and minimum values attained by

Arithmetic/geometric sequences and binomial expansion, find s10 for the ari...

find s10 for the arithmetic sequenxe inwhich a1=5 and a10=68

Determine the exterior angle, Using the sketch below and the fact that ∠A +...

Using the sketch below and the fact that ∠A + ∠B + ∠C + ∠D = 325, Determine m∠E.   a. 81° b. 35° c. 25° d. 75° b. The addition of the measures of the exterio

Quadaric equation, two numbers differ by 7 and have a product of 120.what a...

two numbers differ by 7 and have a product of 120.what are they ?

Supply/demand, For the pair of supply-and-demand equations, where x represe...

For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equ

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