# MATH 2301-102 Fall 2018 Calculus I Recitation 4 Week 6

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

1. Compute the following derivatives:
1. $$\displaystyle \frac{d}{dx} \left[3\sin(x)\right]=$$
2. $$\displaystyle \frac{d}{dx} \left[x\sin(3)\right]=$$
3. $$\displaystyle \frac{d}{dx} \left[3\sin(3)\right]=$$
4. $$\displaystyle \frac{d}{dx} \left[x\sin(x)\right]=$$
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. $$\displaystyle \frac{d}{dx} \left[(9\cos(x)+x^8+x^5+3)\sin(x)\right]=$$
2. $$\displaystyle y=\frac{x^3+5x}{\sin(x)} \Rightarrow \frac{dy}{dx}=$$
3. $$\displaystyle \frac{d}{dx} \left[\frac{\sin(x)\cos(x)}{x^3+x}\right]=$$
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 $$\displaystyle\left(fg\right)''$$.