Quiz 6 (Solution)

Date: MATH 1210-4 - Spring 2004

Use properties to find:

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

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

   
   

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

   We use the chain and the quotient rules:

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

   
   

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

   We use the chain rule:

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