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

Integration, what is integration and how is it important

what is integration and how is it important

Sketch the graph of h (t ) = 1 - 5e 1/(t/2), Sketch the graph of h (t ) = ...

Sketch the graph of h (t ) = 1 - 5e  1/(t/2) Solution : Let's primary get a table of values for this function. Following is the sketch. The major point behin

A fire in a building b is reported on telephone, A fire in a building B is ...

A fire in a building B is reported on telephone to two fire stations P and Q, 10km apart from each other on a straight road.  P observes that the fire is at an angle of 60 o to th

Calculate the area of the ade and compare it with abc, The vertices ...

The vertices of a ? ABC are A(4, 6), B(1. 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that AD/AB = AE/AC = 1/4 .Calculate the  ar

Problem on numbers, # In a two-digit, if it is known that its unit''s digi...

# In a two-digit, if it is known that its unit''s digit exceeds its ten''s digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the

Quadratic equation, If roots of (x-p)(x-q) = c are a and b what will be th...

If roots of (x-p)(x-q) = c are a and b what will be the roots of (x-a)(x-b) = -c    please explain? Ans) (x-p)(x-q)=c x2-(p+q)x-c=0 hence,   a+b=p+q  and      a.b=pq-c

Regression, regression line drawn as Y=C+1075x, when x was 2, and y was 239...

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Interpretation, Interpretation A high value of r as +0.9 or - 0...

Interpretation A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that there is a causal relationship that is

Differentials, Differentials : In this section we will introduce a nota...

Differentials : In this section we will introduce a notation. We will also look at an application of this new notation. Given a function y = f ( x ) we call dy & dx differen

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