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

Intervals of validity, I've termed this section as Intervals of Validity si...

I've termed this section as Intervals of Validity since all of the illustrations will involve them. Though, there is many more to this section. We will notice a couple of theorems

Numerical methods for ordinary differential equationsordinay, #k1=f(Tn, Xn)...

#k1=f(Tn, Xn), k2=f (Tn + H.Y,Xn + H.Y.k1) Xn+1=Xn + H(a.k1+ b.k2) Find a relation between Y,a and b so that the method is second order consistent.

Explain adding negative fraction, Explain Adding Negative Fraction? To...

Explain Adding Negative Fraction? To add negative fractions: 1. Find a common denominator. 2. Change the fractions to their equivalents, so that they have common denominators

Find out the slope of equations, Example:  find out the slope of equations ...

Example:  find out the slope of equations and sketch the graph of the line.                         2 y - 6x = -2 Solution To get the slope we'll first put this in slope

Calculate the total surface area which is exposed , A golf ball has a diame...

A golf ball has a diameter equal to 4.1cm. Its surface has 150 dimples each of radius 2mm. Calculate the total surface area which is exposed to the surroundings assuming that the d

How much, If one acre costs $2500 how much does .39 of an acre cost

If one acre costs $2500 how much does .39 of an acre cost?

#title.heat loss in a cylindrical pipe., briefly explain how the famous equ...

briefly explain how the famous equation for the loss of heat in a cylindrical pipe is derived

Comercial maths, solve a trader purchases coffee at the rate of Rs. 350 per...

solve a trader purchases coffee at the rate of Rs. 350 per kg and mixes it with chicory bought at the rate of Rs.750 per kg in the ratio 5:2.If he sells the mixture at the rate of

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