## anonymous 4 years ago What's the derivative of (sin(x))^(57)?

1. Directrix

57 [ sin(x) ] ^ (56) [ cos(x) ]

2. anonymous

3. Directrix
4. anonymous

chain rule: $(\sin(x))^{57}=57(\sin(x))^{56}\times \cos(x)$

5. Directrix

Starlight says that answer is incorrect. I think it is correct - just a notational difference in writing (sin (x) ) ^ 57.

6. anonymous

$g(x) = x ^{57}$$f(x)=\sin (x)$$g(f(x))=(\sin (x))^{57}$$g \prime(f(x)) = g \prime(f(x))f \prime(x)$$g \prime(f(x))=57(\sin(x))^{56}\times \cos(x)$

7. anonymous

I don't know but it was cos(x) lol... http://www.wolframalpha.com/input/?i=57th+derivative+of+sin%28x%29 and thanks