For each of the composite functions, identify an inside function and an outside function and write the derivative with respect to x of the composite function.

Question

Quizplus · Accepted Answer

Derivative: (e^x)(3x^2)

B) Inside Function: 3x+1; Outside Function: ln(x)
Derivative: (1/x)(3)

C) Inside Function: x^2-1; Outside Function: sqrt(x)
Derivative: (1/2sqrt(x))(2x)

D) Inside Function: 2x-1; Outside Function: cos(x)
Derivative: -sin(2x-1)(2)

E) There is no inside and outside function, so the question does not make sense in this case.

Answer: A, B, C 
 A, B, and C are the only options with clearly identifiable inside and outside functions. D has identifiable inside and outside functions but requires knowledge of the derivative of cosine. E is not a valid option since there is no inside and outside function.

For Each of the Composite Functions, Identify an Inside Function