Question

for y=4sin(3x), find y(pi)

Answer 1

plug in pi for x

Answer 2

oh wait sorry that's supposed to be y'(pi)

Answer 3

ok so you have to find the derivative of 4 sin3x

Answer 4

oh wait i think i got it can you check if this is right

Answer 5

ok

Answer 6

y'=4cos(3x)(3) ?

Answer 7

yea or you could write it as 12 cos (3x)

Answer 8

thanks! may i ask, is this always the right way, because at first i thought i would use the chain rule on 4 and sin(3x)

Answer 9

sin (3x) is a compound function Ignore the 4 at first - just use chain rule on sin 3x . Finally multiply the result by 4.

Answer 10

oh, so should i just ignore numbers that appears before the trig function? i should just do what's inside the funtion?

Answer 11

yes - but of course dont forget to operate on them after you have done the differentiation

Answer 12

eg
2 cos 3x = 2 * -3sin 3x = -6 sin 3x

Answer 13

yes, thanks! oh wait, last one, may you answer this? i think the answer is 0 but not sure

Answer 14

y=1-2u
u = x^3 - 2x^2 + 6

find y''(x=1)

Answer 15

y = 1 - 2(x^3 - 2x^2 + 6)
y = 1 - 2x^3 + 4x^2 - 12

what do you get for y' ?