Question

HELP! PLEASE EXPLAIN! MEDAL! URGENT!
@amistre64 @dan815 @pooja195

Answer 1

@amistre64 @freckles

Answer 2

first principles ...

Answer 3

I already know what the answer is. I just don't know how to get it.

Answer 4

use the formula for cos(a+b)

Answer 5

uhh ..... ^7 ?? lol

Answer 6

OH! I didn't think of that...
sin(x)cos(h) + cos(x)sin(h)
?

Answer 7

almost, but no ...

cos(x+h) = cos(x)cos(h) - sin(x)sin(h)

but its easy to confuse them

Answer 8

Ah. So how do I apply the chain rule to (cos(x)cos(h) - sin(x)sin(h))^7?

Answer 9

(a+b)^7 = (7 0) a^7 + (7 1) a^6b + (7 2) a^5b^2 + ...

Answer 10

binomial thrm i believe its called

Answer 11

???

Answer 12

gonna have to expand it out unless you know of some other way to approach it

Answer 13

So you couldn't apply the chain rule to the entire thing as one?

Answer 14

\[(a+b)^7=\sum_{n=0}^{7}\binom{7}{n}a^{7-n}b^n\]
chain rule is not a 'first principles' application ... rules are the results of the limiting process, not the basis for them.

Answer 15

is your attempt to work this out with the limiting process, or to see it as a function that you can apply the rules to?

Answer 16

\[\cos C-\cos D=-2\sin \frac{ C+D }{ 2 }\sin \frac{ C-D }{ 2 }\]

Answer 17

does that apply well to the power of 7?

Answer 18

i dont really understand but i have to go right now
be back later

Answer 19

\[\left( x+h \right)^7=C,x^7=D\]

Answer 20

cx^7 ch^7
-7cx^6 ch^6 sx sh
+21cx^5 ch^5 sx^2 sh^2
-35 cx^4 ch^4 sx^3 sh^3
+35 cx^3 ch^3 sx^4 sh^4
-21 cx^2 ch^2 sx^5 sh^5
+7 cx ch sx^6 sh^6
-sx^7 sh^7
-cx^7
all divided by h

cx *
cx^6 ch^7
-7cx^5 ch^6 sx sh
+21 cx^4 ch^5 sx^2 sh^2
-35 cx^3 ch^4 sx^3 sh^3
+35 cx^2 ch^3 sx^4 sh^4
-21 cx ch^2 sx^5 sh^5
+7 ch sx^6 sh^6
-sx^7 sh^7
-cx^6
all divided by h

recall what the limits of cn/n and sn/n are?