(a) For the function : (i) Express the derivative as a limit involving . (ii) Show,…

MATHEMATICS · Subjective · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

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)

x=\frac{\pi}{3}