Diffrentiation, Mathematics

Assignment Help:

y=f(a^x)   and f(sinx)=lnx find dy/dx

Solution) dy/dx = (a^x)(lnx)f''(a^x), .........(1)

but f(sinx) = lnx implies f(x) = ln(arcsinx)

hence f''(x) = (1/arcsinx) (1/ ( ( 1-x^2 ) ^ ( !/2 ) ) implies f''(a^x) = (1/arcsin(a^x)) (1/ ((1-a ^ (2x)) ^ (1/2))) ............(2)

hence from ...(1) &.....(2) the solution is obtained but it should br noted that the given solution exist only when x belongs to (0,1].


Related Discussions:- Diffrentiation

Find out equation is a function, Example: Find out which of the following ...

Example: Find out which of the following equations functions are & which are not functions.                            y= 5x + 1 Solution The "working" definition of fu

Payoff Matrix, A farmer grows apples on her 400-acre farm and must cope wit...

A farmer grows apples on her 400-acre farm and must cope with occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown"

Index numbers, What are advantages and disadvantages of both Laspeyres and ...

What are advantages and disadvantages of both Laspeyres and Paasche?

Find out the average temperature, Find out the average temperature: E...

Find out the average temperature: Example: Find out the average temperature if the subsequent values were recorded: 600°F, 596°F, 597°F, 603°F Solution: Step

Basic computation formulas of differentiation, Basic "computation" formulas...

Basic "computation" formulas : Next, let's take a quick look at some basic "computation" formulas that will let us to actually compute some derivatives. Formulas 1)   If f

Debate over answer to an equation..., The math equation is written exactly ...

The math equation is written exactly this way: 0+50x1-60-60x0+10=??? The answer I get is 10 and others say 0 0+50=50 50x1=50 50-60=-10 -10-60=-70 -70x0=0 0+10=10

Find where the breakdown occurred and his original speed, A cyclist, after ...

A cyclist, after riding a certain distance, stopped for half an hour to repair his bicycle, after which he completes the whole journey of 30km at half speed in 5 hours.  If the bre

Trigonometry, A 25 foot ladder just reaches the top of a house and forms an...

A 25 foot ladder just reaches the top of a house and forms an angle of 41.5 degrees with the wall of the house. How tall is the house?

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