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

How many more cm are required to reach the average monthly, Thomas is remai...

Thomas is remaining track of the rainfall in the month of May for his science project. The first day, 2.6 cm of rain fell. On the second day, 3.4 cm fell. On the third day, 2.1 cm

Matrix, matrix of [1 4 ] [a b]=4/9

matrix of [1 4 ] [a b]=4/9

Surds, solve for x: logx9

solve for x: logx9

Find the area irrigated by this system, An irrigation system uses a straigh...

An irrigation system uses a straight 30m sprinkler pipe which is capped at one end and arranged so that all water is released directly downwards and pivots around a central point.

MATLAB, Program of "surface of revolution" in MATLAB

Program of "surface of revolution" in MATLAB

Solve the form x2 - bx + c, The form x2 - bx + c ? This tutorial will ...

The form x2 - bx + c ? This tutorial will help you factor quadratics that look something like this: x 2 -7x + 12 (No leading coefficient; negative middle coefficient; p

Show that cos12+cos60+cos84=cos24+cos48 , L.H.S. =cos 12+cos 60+cos 84 =c...

L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12   R.H.S =c

difference between two sample means (large sample), Testing The Difference...

Testing The Difference Between Two Sample Means (Large Samples) A large sample is defined as one which have 30 or more items as n≥30 whereas n is the sample size In a busine

Functions, the function g is defined as g:x 7-4x find the number k such tha...

the function g is defined as g:x 7-4x find the number k such that kf(-8)=f- 3/2

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