Consider the composite function

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

y=f(g(h(x)))

, where

f, g

and

h

are differentiable functions of a real variable. (i) Define a composite function in the given context. (ii) If

u=h(x)

and

v=g(u)

, express the differentials

dy, dv

and

du

in terms of the corresponding derivatives and the differential

dx

. Write the relation linking these three differentials. (iii) Hence obtain an explicit formula for

\dfrac{dy}{dx}

in terms of

f'(g(h(x)))

g'(h(x))

and

h'(x)