For the given pair of functions, write the composite function and its derivative in terms of one input variable.
A) ;
B) ;
C) ;
D) ;
E) ;

Question

For the given pair of functions, write the composite function and its derivative in terms of one input variable. 
A) ; 
B) ; 
C) ; 
D) ; 
E) ;

Quizplus · Accepted Answer

The composite function is f(g(x)) where f(x) = e^x and g(x) = ln(x). 
So, the composite function is f(g(x)) = e^(ln(x)) = x. 
The derivative of f(g(x)) is the derivative of x, which is 1. 
Therefore, the derivative is 1.

For the Given Pair of Functions, Write the Composite Function