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Thread: Differentiation

  1. #1
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    Differentiation

    Check my answers please

    1. $\displaystyle f(x)=sin\frac 1{x}$
    MY answer: $\displaystyle -\frac 1{x^2}cos\frac 1{x}$

    2. $\displaystyle m(x)=e^xsinx$
    My answer: $\displaystyle e^xcosx+e^xsinx$

    3. $\displaystyle f(x)=ln(x^3-x+9)$
    My answer: $\displaystyle \frac {3x^2+1}{x^3-x+9}$

    4. $\displaystyle f(x)=ln(e^x+1)$
    My answer: $\displaystyle \frac {e^x}{e^x+1}$

    5. $\displaystyle u(x)=x arctan x$
    My answer: $\displaystyle arctanx+\frac x{x^2+1}$

    6. $\displaystyle v(x)=artan(x+1)$
    My answer: $\displaystyle \frac 1{(x+1)^2+1}$
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  2. #2
    Super Member
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    Quote Originally Posted by jkami View Post
    Check my answers please

    1. $\displaystyle f(x)=sin\frac 1{x}$
    MY answer: $\displaystyle -\frac 1{x^2}cos\frac 1{x}$

    2. $\displaystyle m(x)=e^xsinx$
    My answer: $\displaystyle e^xcosx+e^xsinx$

    3. $\displaystyle f(x)=ln(x^3-x+9)$
    My answer: $\displaystyle \frac {3x^2+1}{x^3-x+9}$

    4. $\displaystyle f(x)=ln(e^x+1)$
    My answer: $\displaystyle \frac {e^x}{e^x+1}$

    5. $\displaystyle u(x)=x arctan x$
    My answer: $\displaystyle arctanx+\frac x{x^2+1}$

    6. $\displaystyle v(x)=artan(x+1)$
    My answer: $\displaystyle \frac 1{(x+1)^2+1}$
    Number 3) should be $\displaystyle \frac {3x^2-1}{x^3-x+9}$, everything else is correct.
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