A function is defined by

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

g(x)=k\sin(mx)

, where

k

and

m

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

g'(x)

in terms of

k

m

and

x

. (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)

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

k

and

m

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

Related theory

Advanced Differentiation
Differentiation Rules
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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