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

Explain simplifying rational expressions, Explain Simplifying Rational Expr...

Explain Simplifying Rational Expressions ? A rational expression, or algebraic fraction, is an expression in which you have a polynomial divided by a polynomial. Sometimes it

Partial differential equations, I need expert who can solve 10 set of PDE w...

I need expert who can solve 10 set of PDE with constant of integration.

Rates, we dont know how to do rates

we dont know how to do rates

The blood pressure over two heart beats, At rest, the human heart beats onc...

At rest, the human heart beats once every second. At the strongest part of the beat, a person's blood pressure peaks at 120mmHg. At the most relaxed part of the beat, a person's bl

Reduce the rational expression to lowest terms, Reduce the following ration...

Reduce the following rational expression to lowest terms.                                     x 2 - 2 x - 8/ x 2 - 9 x + 20 Solution When reducing a rational expressio

If 1/x+2, if 1/x+2, 1/x+3, 1/x+5 are in AP find x Ans 1/x+2,1/x+3, 1/x+5...

if 1/x+2, 1/x+3, 1/x+5 are in AP find x Ans 1/x+2,1/x+3, 1/x+5 are in AP find x. 1/x+3 - 1/x+2 = 1/x+5-1/x+3 =>  1/x 2 +5x+6  = 2/ x 2 +8x +15 =>  On solving we get x

Array -categories of multiplication, Array - when items are arranged in a ...

Array - when items are arranged in a regular rectangular pattern of rows and columns, counting how many there are. (e.g., if there are 3 rows of 5 girls each, how many girls are t

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