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Differentiating trigonometric functions Watch

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    How would you differentiate:

    y=cosx^2
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    (Original post by monstercable)
    How would you differentiate:

    y=cosx^2
    Is that (cosx)^2 or cos(x^2)

    either way ... chain rule as you have a function of a function
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    (Original post by monstercable)
    How would you differentiate:

    y=cosx^2
    Chain rule
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    It's cos(x^2). Okay thank you, i'll give it a go
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    Okay, I still can't do it :s
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    You can use the chain rule with u = x^2

    Setup up the chain rule  \frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}

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    Or you could notice learn a rule that I have used.

     \frac{d}{dx}(cos f(x)) = -f'(x) sin f(x)

    Much the same as other trig functions this works for

    \frac{d}{dx}(sin f(x)) = f'(x) cos f(x)
    - I suggest you do the chain rule method first, as this is probably the method they want you to use, but for future reference the formulas are there and are simple to remember.
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    (Original post by insparato)
    You can use the chain rule with u = x^2

    Setup up the chain rule  \frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}

    Spoiler:
    Show
    Or you could notice learn a rule that I have used.

     \frac{d}{dx}(cos f(x)) = -f'(x) sin f(x)

    Much the same as other trig functions this works for

    \frac{d}{dx}(sin f(x)) = f'(x) cos f(x)
    - I suggest you do the chain rule method first, as this is probably the method they want you to use, but for future reference the formulas are there and are simple to remember.
    Okay so is this the right answer:

    y= cos(x^2)

    Let U = (x^2), therefore DU/DX = 2x
    Y= CosU, therefore DY/DU= -SinU
    Therefore, DY/DX = -2XSin(X^2)


    Thank you by the way!
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    (Original post by monstercable)
    Okay so is this the right answer
    Yes.
 
 
 
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