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Math Help - Another Chain Rule Question.

  1. #1
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    Another Chain Rule Question.

    f(x)= sin^4(x)

    What does 'u' in this situation equal?

    sin(x) or  x^4
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  2. #2
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    d/dx(x^n)=nx^(n-1)dx/dx

    Quote Originally Posted by Zanderist View Post
    f(x)= sin^4(x)

    What does 'u' in this situation equal?

    sin(x) or  x^4
    f'(x)=4sin^3xcosx

    the chain rule is a mere technical jargon!
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  3. #3
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    Quote Originally Posted by Zanderist View Post
    f(x)= sin^4(x)

    What does 'u' in this situation equal?

    sin(x) or  x^4
    u is always the "internal" function. Here, to evaluate sin^4(x) you would first evaluate sin(x) then take the fourth power. If you let u= sin(x) then f(x)= u^4
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    I'd like to add on to this.

    What are the steps to:

    f(x)=7cos(cos(x))
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  5. #5
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    Quote Originally Posted by Zanderist View Post
    I'd like to add on to this.

    What are the steps to:

    f(x)=tan 4x
    \frac{d}{dx} \tan{u} = \sec^2{u} \cdot \frac{du}{dx}<br />


    ... in future, start a new problem with a new thread.

    more examples of the chain rule ...

    http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html
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  6. #6
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    Quote Originally Posted by Zanderist View Post
    I'd like to add on to this.

    What are the steps to:

    f(x)=7cos(cos(x))
    f(x) = 7\cos{u}

    f'(x) = -7\sin{u} \cdot \frac{du}{dx}
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