1. ## Differentiation

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: $\displaystyle \frac 1{(x+1)^2+1}$

2. Originally Posted by jkami

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.