Related Rates Quiz

$$\frac{\text{d}}{\text{d}x}\left[u\left(x\right)\pm v\left(x\right)\right]=\frac{\text{d}}{\text{d}x}\left[u\left(x\right)\right]\pm\frac{\text{d}}{\text{d}x}\left[v\left(x\right)\right]$$

$$\frac{\text{d}}{\text{d}x}\left[u\left(x\right)\cdot v\left(x\right)\right]=v\left(x\right)\cdot\frac{\text{d}u}{\text{d}x}+u\left(x\right)\cdot\frac{\text{d}u}{\text{d}x}$$

$$\frac{\text{d}}{\text{d}x}\left[x^n\right]=n\cdot x^{n-1}$$

$$\frac{\text{d}}{\text{d}x}\left[\frac{u\left(x\right)}{v\left(x\right)}\right]=\frac{v\left(x\right)\cdot\frac{\text{d}u}{\text{d}x}-u\left(x\right)\cdot\frac{\text{d}u}{\text{d}x}}{v\left(x\right)^2}$$

For $$y=u\left(x\right)$$ , $$\frac{\text{d}y}{\text{d}x}=\frac{\text{d}y}{\text{d}u}\cdot\frac{\text{d}u}{\text{d}x}$$

$$\frac{\text{radians}}{\text{second}}$$  

$$\text{radians}$$  

$$\text{meters}$$  

$$\frac{\text{kilometers}}{\text{hour}}$$  

$$\text{kilograms}\$$  

$$\text{seconds}$$  

$$\frac{\text{meters}}{\text{seconds}^2}$$  

$$\text{kilograms}\cdot\frac{\text{meters}\ }{\text{seconds}^2}$$  

$$\frac{\text{Joules}}{\text{Coulomb}}$$  

$$\frac{-\frac{18}{5}in}{hr}$$  

$$\frac{-\frac{17}{5}in}{hr}$$  

$$-18\ \frac{in}{hr}$$  

$$-3\ \frac{in}{hr}$$  

$$\frac{\frac{2}{3}m}{\min}$$  

$$\frac{1m}{\min}$$  

$$\frac{\frac{1}{3}m}{\min}$$  

$$\frac{\frac{7}{3}m}{\min}$$  

$$42\pi\ \frac{in^3}{\sec}$$

$$39\pi\frac{in^3}{\sec}$$

$$22\pi\ \frac{in^3}{\sec}$$

$$32\pi\frac{in^3}{\sec}$$

$$76\pi\ \frac{cm^2}{\min}$$

$$72\pi\frac{cm^2}{\min}$$

$$77\pi\frac{cm^2}{\min}$$

$$62\pi\frac{cm^2}{\min}$$

3 ft/sec

7.2 ft/sec

-12 ft/sec

-7.2 ft/sec