Question

how do you find the derivative of alpha?? (attached)

Answer 1

Chain rule.

Answer 2

you want the derivative of k with respect to alpha

Answer 3

\(\sin^7(x)\cos^3(x)\) use the product rule and the chain rule.
\(7\sin^6(x)\cos(x)\cos^3(x)+\sin^7(x)3\cos^2(x)(-\sin(x))\)

Answer 4

Product rule + chain rule

Answer 5

product rule then chain rule

Answer 6

simplify....

Answer 7

pray that you get it correctly

Answer 8

so sin^6(alpha)cos^3(alpha)(5cos(alpha)^3?

Answer 9

or do i write it in terms of x

Answer 10

aw it says its wrong :(

Answer 11

so f(x) is (cos(x))3⋅(sin(x))7

Answer 12

and d/dx would be 7⋅(cos(x))4⋅(sin(x))6−3⋅(cos(x))2⋅(sin(x))8

Answer 13

im still wrong..

Answer 14

wait should i write that in terms of x or alpha? (x was wrong)

Answer 15

alpha

Answer 16

is my answer correct though?

Answer 17

7⋅(cos(x))^4⋅(sin(x))^6−3⋅(cos(x))^2⋅(sin(x))^8?