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

Factoring trinomial, what is the factor of the trinomial 2x2-7x-4

what is the factor of the trinomial 2x2-7x-4

Positive skewness-measure of central tendency, Positive Skewness - It ...

Positive Skewness - It is the tendency of a described frequency curve leaning towards the left. In a positively skewed distribution, the long tail extended to the right. In

How to subtract fractions with the same denominators, Q. How to Subtract fr...

Q. How to Subtract fractions with the same denominators? Ans. Subtracting fractions is basically the same as adding them. If you don't know how to add fractions, you shoul

Determine the size of the proposed repayments, Five years ago a business bo...

Five years ago a business borrowed $100,000 agreeing to repay the principal and all accumulated interest at 8% pa compounded quarterly, 8 years from the loan date. Two years after

Definition of inverse functions, Definition of inverse functions :  Given...

Definition of inverse functions :  Given two one-to-one functions f ( x ) and g ( x ) if ( f o g ) ( x ) = x  AND  ( g o f ) ( x ) = x then we say that f ( x ) & g ( x ) are i

Vector analysis ...gradient, A body is constrained to move in a path y = 1+...

A body is constrained to move in a path y = 1+ x^2 and its motion is resisted by friction. The co-efficient of friction is 0.3. The body is acted on by a force F directed towards t

Shares, a person having rs.10 shares of value rs.6000 in a company which pa...

a person having rs.10 shares of value rs.6000 in a company which pays a 7% dividend invested the money gained by selling those shares and bought rs.25 shares at rs.24 per share in

Linear programming, what is the advantage of dual linear problem programmin...

what is the advantage of dual linear problem programming when we maximize profit then what is need to minimize cost of the same problem

Indices, What is a way to solve indices

What is a way to solve indices

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