See the coversheet for instructions and the point value of each problem.
- Compute the following derivatives:
- \(\displaystyle \frac{d}{dx} \left[3\sin(x)\right]=\)
- \(\displaystyle \frac{d}{dx} \left[x\sin(3)\right]=\)
- \(\displaystyle \frac{d}{dx} \left[3\sin(3)\right]=\)
- \(\displaystyle \frac{d}{dx} \left[x\sin(x)\right]=\)
- \(\displaystyle \frac{d}{dx}\left[\frac{\sin(x)}{3}\right]=\)
- \(\displaystyle \frac{d}{dx}\left[\frac{\sin(3)}{x}\right]=\)
- \(\displaystyle \frac{d}{dx}\left[\frac{\sin(3)}{3}\right]=\)
- \(\displaystyle \frac{d}{dx}\left[\frac{\sin(x)}{x}\right]=\)
- Compute the following derivatives:
- \(\displaystyle \frac{d}{dx} \left[(9\cos(x)+x^8+x^5+3)\sin(x)\right]=\)
- \(\displaystyle y=\frac{x^3+5x}{\sin(x)} \Rightarrow \frac{dy}{dx}=\)
- \(\displaystyle \frac{d}{dx} \left[\frac{\sin(x)\cos(x)}{x^3+x}\right]=\)
-
- Use the Product Rule twice to prove that if \(f\), \(g\), and \(h\) are differentiable, then \((fgh)'=f'gh+fg'h+fgh'\).
- Find the corresponding formula for \(\displaystyle\left(\frac{f}{gh}\right)'\).
- Find the corresponding formula for \(\displaystyle\left(fg\right)''\).
Last modified: Thu Sep 27 18:37:37 UTC 2018