Mathematics

Problem

A function is defined by

g(x)=k\sin(mx)

, where

k

and

m

are non-zero real constants. a. (i) Obtain a simplified formula for

g'(x)

in terms of

k

m

and

x

. b. (ii) Using the result of part (i), find

g'(x)

when

k=3

and

m=\pi

, and hence compute

g'\!\left(\dfrac{\pi}{6}\right)

.},{ c. (iii) Comment on how the constants

k

and

m

influence the amplitude and frequency of the derivative function compared with the original function.