Differentiate y = x x using implicit differentiation, Mathematics

Assignment Help:

Differentiate y = x x

Solution : We've illustrated two functions similar to this at this point.

d ( xn ) /dx = nxn -1                                d (a x ) /dx= a x ln a

Neither of these two can imply here since both need either the base or the exponent to be a constant.  In this case the base and the exponent both are variables and thus we have no way to differentiate this function by using only known rules from earlier sections.

However, with logarithmic differentiation we can do this.  First take logarithm of both sides and utilize the logarithm properties to simplify things a little.

ln y = ln x x

ln y = x ln x

Differentiate both sides by using implicit differentiation.

                               y′ / y = ln x + x ( 1 /x)= ln x + 1

As along the first example multiply through y & substitute back in for y.

y′ = y (1 + ln x )

= x x (1 + ln x )

We'll close this section out with a quick recap of all the various ways we've seen of differentiating functions along with exponents.  It is significant to not get all of these confused.


Related Discussions:- Differentiate y = x x using implicit differentiation

Finite math, Find the present value of an ordinary annuity which has paymen...

Find the present value of an ordinary annuity which has payments of 2300 per year for 15 years at 6% compounded annually

Find distance between points (b + c, Find the distance between the points (...

Find the distance between the points (b + c, c + a) and (c + a, a + b) . Ans : Use distance formula

Why x and y are simplifying expressions, Why x and y are Simplifying Expres...

Why x and y are Simplifying Expressions? You're doing algebra now, and you know you're going to see x's and y's. But before we work with x's and y's, we'll explore why we use t

Linear programming, #question.areas of applications of linear program mes t...

#question.areas of applications of linear program mes to solution to engineering problems.

Explain how to converting percents to decimals , Explain how to Converting ...

Explain how to Converting Percents to Decimals ? Percent : "Percent" means "per hundred." Percents are represented by a percent sign ( % ) to the right of a number.  For exam

Define natural numbers, Q. Define natural numbers Ans. The natural...

Q. Define natural numbers Ans. The natural numbers (also called the counting numbers) are the numbers that you "naturally" use for counting: 1,2,3,4,... The set of n

Identify the flaw in the argument, Identify the flaw in the following argum...

Identify the flaw in the following argument which supposedly determines that n 2 is even when n is an even integer. As well name the reasoning:             Assume that n 2 is

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