Let be a non-zero real constant and let for all such that is defined.

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

k

be a non-zero real constant and let

f(x)=\tan(kx)

for all

x

such that

\tan(kx)

is defined. (a) Write

f(x)

entirely in terms of

\sin(kx)

and

\cos(kx)

. Then compute

f'(x)

by differentiating that expression. (b) Show that your result in part (a) can be rewritten in the simplified form

f'(x)=k\sec^{2}(kx)