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

Imaginay Number, how to solve imaginary number such as like (-3v-5)² ?? Can...

how to solve imaginary number such as like (-3v-5)² ?? Can I cancel the radical sign and the power of two ? and square the -3 and times to -5 ? hope you will answer this :) thanks

Boundary value problem, solve the in-homogenous problem where A and b are c...

solve the in-homogenous problem where A and b are constants on 0 ut=uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)

Undetermined coefficients, In this section we will see the first method whi...

In this section we will see the first method which can be used to find an exact solution to a nonhomogeneous differential equation. y′′ + p (t ) y′ + q (t ) y = g (t) One of

Help with individual questions, Hi, I''m looking for assistance/solutions t...

Hi, I''m looking for assistance/solutions to individual questions. I''ve already answered them but seek confirmation my answers are correct. I don''t want answers to a complete e

Example of multiplication of complex numbers, Multiply following and write ...

Multiply following and write the answers in standard form.  (a) 7 i ( -5 + 2 i )  (b) (1 - 5 i ) ( -9 + 2 i ) Solution (a) Thus all that we have to do is distribu

Find sampling interval - horizontal and vertical asymptote, In a digital fi...

In a digital filter, one of the parameters in its difference equation is given by the formula a) Show that the above formula has one horizontal and one vertical asymptote.

Working definition of limit - sequences and series, Working Definition of L...

Working Definition of Limit 1. We state that if we can create an as close to L like we want for all adequately large n.  Alternatively, the value of the a n 's approach

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