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

Pre-calculus, Give all solutions between o degree and 360 degree for sin x=...

Give all solutions between o degree and 360 degree for sin x=3/2

Differential calculus, lim n tends to infintiy ( {x} + {2x} + {3x}..... +{n...

lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x? Ans) all no.s are positive or 0. so limit is either positive

Describe the types of triangles, Describe the Types of triangles ? Tria...

Describe the Types of triangles ? Triangles can be classified according to the lengths of the sides or the measures of the angles. 1. Naming triangles by sides An

Determine series is convergent or divergent by root test, Find out if the f...

Find out if the following series is convergent or divergent. Solution There really is not very much to these problems another than calculating the limit and then usin

Conditional probability - rules of probability, Conditional probability - R...

Conditional probability - Rules of Probability This is the probability associated with combinations of events but given that some prior result has already been achieved with o

Exponents., the (cube square root of 2)^1/2)^3

the (cube square root of 2)^1/2)^3

Geometyr, Lines EF and GH are graphed on this coordinate plane. Which point...

Lines EF and GH are graphed on this coordinate plane. Which point is the intersection of lines EF and GH?

Find the perimeter and the area of the shaded portion, The given figure con...

The given figure consists of four small semicircles and two big semicircles.  If the smaller semicircles are equal in radii and the bigger semicircles are also equal in radii, find

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