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

Mss. Ann, I need marketing management sample assignment as a guide

I need marketing management sample assignment as a guide

Term paper topics, please suggest me that how can i get the term papers top...

please suggest me that how can i get the term papers topics?

The limit, The Limit : In the earlier section we looked at some problems ...

The Limit : In the earlier section we looked at some problems & in both problems we had a function (slope in the tangent problem case & average rate of change in the rate of chan

integration: if f(x)+f(x+1/2) =1 find limit 0 to 2, f(x)+f(x+1/2) =1 f(x...

f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1

Operations research, scope of operation research and its limitations

scope of operation research and its limitations

If tan2x.tan7x=1 , tan9x = (tan7x + tan2x)/(1 - tan7x*tan2x) here its give...

tan9x = (tan7x + tan2x)/(1 - tan7x*tan2x) here its given 1 - tan2x*tan7x= 0 implies tan9x = infinity since tan9x = (3tan3x - tan^3(3x))/(1 - 3tan^2 (3x)) = infinity implies

Objective type , when is the trnscribing process of data preparation irrele...

when is the trnscribing process of data preparation irrelevant ? a)CAPI b) mall panel c) in home interview d) all of them

Rates of change and tangent lines in limits, Rates of Change and Tangent Li...

Rates of Change and Tangent Lines : In this section we will study two fairly important problems in the study of calculus. There are two cause for looking at these problems now.

Area between two curves, Area between Two Curves We'll start with the ...

Area between Two Curves We'll start with the formula for finding the area among y = f(x) and y = g(x) on the interval [a,b].  We will also suppose that f(x) ≥ g(x) on [a,b].

Multiple integrals, how to convert double integral into polar coordinates a...

how to convert double integral into polar coordinates and change the limits of integration

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