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anonymous
 5 years ago
find the derivative of sin^4 (x)
anonymous
 5 years ago
find the derivative of sin^4 (x)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i no that the derivative of sin is cos, but the power of 4 confuses me

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can split it up sin^2x * sin^2x than do power reducing

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d}{dx}\sin^2 x=4 \sin ^3 x .\cos x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Have you learned about the chain rule yet?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Rewrite it as (cosx)^4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ya i learned the chain rule

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just like newone wrote and chain rule it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so it would be 4sinx^3 * cos?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so what happens here is this. you have to use chain rule. soo.... sin^4(x) > 4sin^3(x)cos(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can even check it out in wolframalpha

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so how do i no when to use the chainrule?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0when you have a function inside a function

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so for this question sin is the inside function and 4 is the outside?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0so we have f(g(x))=(sinx)^4 where f(x)=x^4 and g(x)=sinx

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0the chain rule is this f'(g(x))*g'(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok. think about it like this. when you find derivative of x^2 its 2x. we stop right here becuase we note that x is not in any function. say if we have cos(2x) then we have to use chain rule. becuase x is inside another function. so derivative of cos(2x) = sin(2x) = so we derivce the function first. and then we note that we have to further derive x. so we derivce 2x = 2. so we get the final answer cos(2x) = 2sin(2x) chain rule states:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let \[u = (sin\ x) \rightarrow (sin\ x)^4 = u^4\ and\ du/dx = cos\ x\] Following the chain rule we have \[d/dx(u^4) = d/du(u^4) * du/dx= 4u^3 * (\cos\ x) = 4(\sin\ x)^3(\cos\ x)\]
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