Mathematics

Mathematics

Problem

(a) For the function

g(x)=\cos x

: (i) Express the derivative

g'(x)

as a limit involving

h

. (ii) Show, by evaluating the limit, that

\displaystyle \frac{d}{dx}(\cos x)=-\sin x

. (b) Using the result of part (a), determine

\displaystyle \frac{d}{dx}\bigl(\cos(3x)\bigr)

. (c) Find the slope of the tangent to

y=\cos(3x)

at

x=\frac{\pi}{3}

.

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