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

Coprime positive integer, 6 male students and 3 female students sit around ...

6 male students and 3 female students sit around a round table. The probability that no 2 female students sit beside each other can be expressed as a/b, where a and b are coprime p

Coefficients of the equation, If coefficients of the equation ax 2 + bx + ...

If coefficients of the equation ax 2 + bx + c = 0, a ¹ 0 are real and roots of the equation are non-real complex and  a + c (A) 4a + c > 2b (B) 4a + c Please give t

Word problem, A girl has 25 plants in all, 8 of them are tomatos. She has 1...

A girl has 25 plants in all, 8 of them are tomatos. She has 10 more bean plants than pepper plants. How many pepper plants does she have?

Solve 8 cos2 (1 - x ) + 13 cos(1 - x )- 5 = 0 trig function, Solve 8 cos 2 ...

Solve 8 cos 2 (1 - x ) + 13 cos(1 - x )- 5 = 0 . Solution Now, as specified prior to starting the instance this quadratic does not factor.  Though, that doesn't mean all i

Elps in maths, 25 cookies have to be divided equally among 4 children.hw ca...

25 cookies have to be divided equally among 4 children.hw can we use elps to answer this question?

Maclaurin series - sequences and series, Maclaurin Series Before w...

Maclaurin Series Before working any illustrations of Taylor Series the first requirement is to address the assumption that a Taylor Series will in fact exist for a specifi

Hello, I am here to tell you, Alex has a cold.

I am here to tell you, Alex has a cold.

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