Previously, I asked for the derivative of -4cos (0.5x) and got 2sin(0.5x). However, I don't understand how we got the 2. I assume we're using the product rule.

Question

kira_yamato · Answer

Chain rule.
d/dx (-4cos (0.5x)) = -4 (-sin (0.5x)) (0.5) = 2 sin (0.5 x)

campbell_st · Answer

in your question ypu have -4cos(0.5x) 

thuse uses the chain rule   let u = 0.5x     du/dx = 0.5

                                                y = -4cos(u)      dy/du = 4sin(u)

         then using the chain rule its

                                                dy/dx = dy/du * du/dx
                                                            = 4sin(u) * 0.5
                                                             = 2sin(u)

resubstitute u = 0.5x    gives      dy/dx = 2sin(0.5x)

anonymous · Answer

Right, thanks, I have a better idea now. So we still retain -4. Do we always do that when we have a number in front of cos or sin? I originally thought that since it can be written as -4 * cos(0.5x) that -4 is derived into zero.

kira_yamato · Answer

I don't think so... Because it is a constant multiple so it's like
y = k . f(x)
==> dy/dx = k . f'(x)

kira_yamato · Answer

In this case k=-4 and f(x) = cos(0.5x)

anonymous · Answer

Cool, thanks Kira Yamato.

kira_yamato · Answer

僕に感謝する必要はありません