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

Average function value, Average Function Value The average value of a ...

Average Function Value The average value of a function f(x) over the interval [a,b] is specified by, f avg = (1/b-a) a ∫ b f(x) dx Proof We know that the average

Find the length and breadth of the rectangle, The area of a rectangle gets ...

The area of a rectangle gets decreased by 8 m2, if its length  is decreased by 5 m and breadth increased by 3 m. If we enhance  the length by 3 m and breadth by 2 m, the area is en

Theorem to computer the integral, Use green's theorem to computer the integ...

Use green's theorem to computer the integral F . dr where F = ( y^2 + x, y^2 + y) and c is bounded below the curve y= - cos(x),, above by y = sin(x) to the left by x=0 and to the r

What is factoring of polynomials, What is Factoring of Polynomials? Fac...

What is Factoring of Polynomials? Factoring means much the same thing for polynomials as it does for integers. When you multiply several polynomials together, The polyn

Hypothesis testing of the difference between proportions, Hypothesis Testin...

Hypothesis Testing Of The Difference Between Proportions Illustration Ken industrial producer have manufacture a perfume termed as "fianchetto." In order to test its popul

Facts regarding linear equations, To solve out linear equations we will mak...

To solve out linear equations we will make heavy use of the following facts. 1. If a = b then a + c = b + c for any c.  All it is saying that we can add number, c, to both sides

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