What is the derivative of...?

Question

(sin(x))^2 and (sin(x))^3

Answer 1

Use the chain rule
(d/dx) (sinx)^2 = 2(sinx)(sinx)' = 2(sinx)(cosx)
(d/dx) (sinx)^3 is similar.

Answer 2

I would say that it is 2(cos(x)) and 3(cos(x))^2 since cos x is ninety degrees out of phase with sin x they are each other's derivatives. Squaring or cubing the whole works just needs to be figured out the standard way. It's been years tho...so maybe you leave the inside function alone and just add the derivative at the end.....what's the rule for this..you must have a book of rules. That second way would make the answer 2(sin(x)) + cos(x) and 3(sin(x))^2 + cos (x)............does any of this make sense to you? Something about a chain rule....yea, TIMES........not PLUS

Answer 3

you use the chain rule, start with the out side box and work your way in.

2(sin(x))^1*cos(x)

3(sin(x))^2*cos(x)

Answer 4

2*sinx(cosx)+3*sin^2x(cosx)

Answer 5

(sin(x))^2 ---> 2sin(x)cos(x)

(sin(x))^3 ---> 3(sin(x))^2cos(x)