Question

what is the derivative of 8sin(4pix)

Answer 1

you know the derivative of \(\sin(x)\)?

Answer 2

-cos(x)

Answer 3

you know the chain rule?

Answer 4

is it (f(g(x))) = f'(g(x))g'(x)

Answer 5

put your two answers together :)

Answer 6

-8cos(4pix)

Answer 7

(4pix)

Answer 8

is 8.cos(4.pi.x) if derived to 4.pi.x
if derived to x:
8.4.pi.cos (4.pi.x)

Answer 9

close...you need to multiply by the derivative of the inside

Answer 10

yes...plus \[\frac{d}{dx}\sin(x)=\cos(x)\]

Answer 11

-32cos(x)

Answer 12

and don't forget the \(\pi\)

Answer 13

so the answer is -32cos(pix)

Answer 14

\[32\pi\cos(4\pi x)\]

Answer 15

8sin(4πx)
( sin u )' = u' cos u
u = 4πx --> u' = 4π
-> 8 * 4π cos (4πx) = 32 π cos (4πx)

Answer 16

Remember the sign is positive :)