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  1. #1
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    derivative

    what is the derivative of cos^2 x
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    Quote Originally Posted by b00yeah05 View Post
    what is the derivative of cos^2 x
    From the chain rule, the answer is -2 \cos x \sin x, which is equivalent to -\sin(2x).
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    hmmm...the part where i get confused is choosing which rule to use. by looking at that i thought it was the product rule...

    How do you know when to use which rule?? i know the quotient rule because its usally something divided by something....
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  4. #4
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    <br />
cos^2 x<br />

    is same as (cos x) multiply (cos x) so you use product rule
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    Quote Originally Posted by b00yeah05 View Post
    hmmm...the part where i get confused is choosing which rule to use. by looking at that i thought it was the product rule...

    How do you know when to use which rule?? i know the quotient rule because its usally something divided by something....
    You use the chain rule when you have a function of a function: y = f(g(x)).
    You use the product rule when you have a product of two functions: y = f(x) times g(x).

    Sometimes both rules can be used.

    y = \cos^2 x can be thought of as a function of a function: y = (\cos x)^2, that is, the square of \cos x. On the other hand .....

    y = \cos^2 x can be thought of as a product of two functions: y = (\cos x) \times (\cos x).

    So in this case it doesn't matter whether you use the chain rule or the product rule.

    However, what would your plan be to differentiate y = \cos^5 x. Repeated use of the product rule? I hope NOT .....
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