Quiz 6 (Solution)


Date: MATH 1210-4 - Spring 2004

Use properties to find:

  1. $ D_x (x^2 \tan(x))$. Using the product rule:

    $\displaystyle D_x (x^2 \tan(x)) = D_x(x^2) \tan(x) + x^2 D_x \tan(x) = 2x \tan(x) + x^2 \sec^2(x).$    

  2. $ ((\frac{x+1}{x-1})^{10})'$.

    We use the chain and the quotient rules:

    \begin{displaymath}\begin{split}((\frac{x+1}{x-1})^{10})' &= 10(\frac{x+1}{x-1})...
...{-2}{(x-1)^2} \\ &= -20 \frac{(x+1)^9}{(x-1)^{11}}. \end{split}\end{displaymath}    

  3. $ \frac{d}{dx} (\sin^3(x)+\cos(3x))$.

    We use the chain rule:

    \begin{displaymath}\begin{split}\frac{d}{dx} (\sin^3(x)+\cos(3x)) &= \frac{d \si...
...{d (3x)}{dx} \\ &= 3 \sin^2(x) \cos(x) -3 \sin(3x). \end{split}\end{displaymath}    



Javier Fernandez 2004-03-08