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

Percentage change, in a sale a clothes shop reduces its prices by 30% a shi...

in a sale a clothes shop reduces its prices by 30% a shirt usually costs £38 how much is it in the sale

Implicit differentiation, Implicit Differentiation : To this instance w...

Implicit Differentiation : To this instance we've done quite a few derivatives, however they have all been derivatives of function of the form y = f ( x ) .  Unluckily not all

Coefficient of determination, Coefficient of Determination It refers t...

Coefficient of Determination It refers to the ratio of the explained variation to the total variation and is utilized to measure the strength of the linear relationship. The s

Which number falls among 5.56 and 5.81, Which number falls among 5.56 and 5...

Which number falls among 5.56 and 5.81? If you add a zero to the end of 5.6 to get 5.60, it is simpler to see that 5.56

Statistical inference, Statistical inference This is the process of dra...

Statistical inference This is the process of drawing conclusions about attributes of a population based upon information contained in a sample or taken from the population.

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