Question

Let's find the derivative of \(f (x) = \sin (a x)\):

\(f' (x) = \lim_{h \rightarrow 0} \frac{\sin (a x + a h) - \sin (a x)}{h}\)

\(f' (x) = \lim_{h \rightarrow 0} \frac{\sin (a x) \cos (a h) + \cos (a x) \sin (a h) - \sin (a x)}{h}\)

\(f' (x) = \lim_{h \rightarrow 0} \sin (a x) \frac{\cos (a h) - 1}{h} + \lim_{h \rightarrow 0} \cos (a x) \frac{\sin (a h)}{h}\)

\(f' (x) =\) \(\cos (a x)\)

Answer 1

see the attachment

Answer 2

\[f'(x) = a\cos(ax)\]

Answer 3

can you explain

Answer 4

?

Answer 5

yes, what is \[\lim_{h \rightarrow 0} \sin (a x) \frac{\cos (a h) - 1}{h} + \lim_{h \rightarrow 0} \cos (a x) \frac{\sin (a h)}{h}\] equal to

Answer 6

im not getting you