(a) Let be a differentiable function. Show that the derivative of the composite…

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

(a) Let

g(x)

be a differentiable function. Show that the derivative of the composite function

E(x)=e^{g(x)}

E'(x)=g'(x)\,e^{g(x)}

. (b) Hence explain why a function of the form

g'(x)\,e^{g(x)}

always possesses an antiderivative of the form

e^{g(x)}+C

, where

C

is a constant of integration.