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    how would you differentiate

    y=sin(In x)

    what rule would you use and why?
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    (Original post by HelloImCool)
    how would you differentiate

    y=sin(In x)

    what rule would you use and why?
    Chain because you have a function inside a function.

    Bonus points if you spot what function is inside which.
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    (Original post by RDKGames)
    Chain because you have a function inside a function.

    Bonus points if you spot what function is inside which.
    thank you .
    ln x is inside sin ? idk lol

    If you don't mind , could you tell me when to use the 3 rules because the responses i get from this forum are totally different from my teacher .


    kind regards,
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    (Original post by HelloImCool)
    thank you .
    ln x is inside sin ? idk lol
    Exactly.

    If you don't mind , could you tell me when to use the 3 rules because the responses i get from this forum are totally different from my teacher .
    The names are self-explanatory.


    You use the product rule when you wish to differentiate an expression that is a PRODUCT of two functions in the form f(x)g(x), e.g. x^2 \sin(x), or e^x \log x

    You use the quotient rule when you wish to differentiate an expression that is a QUOTIENT of two functions in the form \dfrac{f(x)}{g(x)}, e.g. \dfrac{e^x}{\sin(x)}, or \dfrac{x^3+1}{x^5+x^3+x+1}

    You use the chain rule when you wish to differentiate an expression that is a COMPOSITION of two functions in the form f(g(x)), e.g. \sin(x^2), or e^{x^3}


    Is this not what your teacher said...?

    P.S. The quotient rule can often be avoided by simply rewriting \dfrac{f(x)}{g(x)} as f(x)g(x)^{-1} and then using the product rule + chain rule. I.e. \dfrac{x^2}{e^x} = x^2e^{-x}
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    (Original post by RDKGames)
    Exactly.



    The names are self-explanatory.


    You use the product rule when you wish to differentiate an expression that is a PRODUCT of two functions in the form f(x)g(x), e.g. x^2 \sin(x), or e^x \log x

    You use the quotient rule when you wish to differentiate an expression that is a QUOTIENT of two functions in the form \dfrac{f(x)}{g(x)}, e.g. \dfrac{e^x}{\sin(x)}, or \dfrac{x^3+1}{x^5+x^3+x+1}

    You use the chain rule when you wish to differentiate an expression that is a COMPOSITION of two functions in the form f(g(x)), e.g. \sin(x^2), or e^{x^3}


    Is this not what your teacher said...?

    P.S. The quotient rule can often be avoided by simply rewriting \dfrac{f(x)}{g(x)} as f(x)g(x)^{-1} and then using the product rule + chain rule. I.e. \dfrac{x^2}{e^x} = x^2e^{-x}
    Thanks. Really appreciate your help.

    My teacher only said use product rule for 2 functions of x and if you see a division is quotient rule
 
 
 
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