MATH 2301-102 and -103 Fall 2017 Calculus I Recitation 5 Week 5

See the coversheet for instructions and the point value of each problem.

  1. Compute the following derivatives:
    1. \(\displaystyle D_x \left[3\sin(x)\right]=\)
    2. \(\displaystyle D_x \left[x\sin(3)\right]=\)
    3. \(\displaystyle D_x \left[3\sin(3)\right]=\)
    4. \(\displaystyle D_x \left[x\sin(x)\right]=\)
    5. \(\displaystyle \frac{d}{dx}\left[\frac{\sin(x)}{3}\right]=\)
    6. \(\displaystyle \frac{d}{dx}\left[\frac{\sin(3)}{x}\right]=\)
    7. \(\displaystyle \frac{d}{dx}\left[\frac{\sin(3)}{3}\right]=\)
    8. \(\displaystyle \frac{d}{dx}\left[\frac{\sin(x)}{x}\right]=\)
  2. Compute the following derivatives:
    1. \(\displaystyle D_x \left[(9\cos(x)+x^8+x^5+3)\sin(x)\right]=\)
    2. \(\displaystyle y=\frac{x^3+5x}{\sin(x)} \Rightarrow \frac{dy}{dx}=\)
    3. \(\displaystyle D_x \left[\frac{\sin(x)\cos(x)}{x^3+x}\right]=\)
    1. Use the Product Rule twice to prove that if \(f\), \(g\), and \(h\) are differentiable, then \((fgh)'=f'gh+fg'h+fgh'\).
    2. Find the corresponding formula for \(\displaystyle\left(\frac{f}{gh}\right)'\).
    3. Find the corresponding formula for \(\displaystyle\left(fg\right)''\).

Last modified: Tue Sep 19 20:15:40 UTC 2017