Mathematics

Problem

(a) Show that for real constants

a

and

b

, the derivative of

\cos(ax+b)

with respect to

x

-a\sin(ax+b)

. (b) Using the result from part (a), find

\dfrac{d}{dx}\,\cos(7x-5)

. (c) Verify your answer in part (b) by evaluating both the derivative formula and the numerical derivative at

x=\dfrac{\pi}{7}

and showing that they agree.