Diffrentiation, Mathematics

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].

Posted Date: 3/9/2013 5:29:38 AM | Location : United States







Related Discussions:- Diffrentiation, Assignment Help, Ask Question on Diffrentiation, Get Answer, Expert's Help, Diffrentiation Discussions

Write discussion on Diffrentiation
Your posts are moderated
Related Questions
dora and her family are driving to visit relatives for the holidays they travel 174 miles in 3 hours if they travel at a constant speed how many miles do they travel in one hourest

This question is in the form of an exercise and questions designed to give you more insight into signal processing. On the Moodle site for the module there is an EXCEL file called

A ride in a taxicab costs $1.25 for the first mile and $1.15 for each additional mile. Which of the following could be used to computed the total cost y of a ride which was x miles

what is 24566x12567=

Children Learn By Experiencing Things : One view about learning says that children construct knowledge by acting upon things. They pick up things, throw them, break them, join the

Before going further, let us repeat an aspect of learning which is useful to keep in mind while formulating teaching strategies. A child who can add or subtract in the context of s

Adding Rational Expressions with Common Denominators To add or subtract fractions or rational expressions with common denominators, all you do is add or subtract the numerators

Frequently, tests that yield abnormal results are repeated for confirmation.  What is the probability that for a usual person a test will be at least 1.5 times as high as the upper

Mike can jog 6.5 miles per hour. At this rate, how many miles will he jog in 30 minutes? Thirty minutes is half an hour. Thus, divide the number of miles Mike can jog in one ho

Graph for the Sequence First we wish to think about the term graphing a sequence. To graph the sequence {a n } we plot the points {n, a n } as n ranges over every possible valu