# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-calculus-chain-quotient.html


## Chain and the other Rules

"Love can reach the same level of talent, and even genius, as the discovery of differential calculus. " Lev Vygotsky


#### Chain rule


##### What you have to know:

- The derivatives of all known functions (If not, check this lesson)
- Recognize all the basic functions
- You must be able to manipulate exponential expressions. (If not, check this lesson)
- You must be able to manipulate logarithmic expressions. (If not, check this lesson)

##### Key Points

- 1. Watch the video:
- 2. Check out this presentation .
- 3. Watch this video .

#### Solved examples


##### Watch the videos


##### Chain rule for simple functions

- 1. Watch the video:
- 2. Watch this video .

#### Product Rule


##### What you have to know:

- The derivatives of all known functions (If not, check this lesson)
- Recognize all the basic functions
- You must be able to manipulate exponential expressions. (If not, check this lesson)
- You must be able to manipulate logarithmic expressions. (If not, check this lesson)

##### Key Points

- 1. Watch the video:
- 2. Check out this presentation .
- 3. Watch this video .

#### Quotient Rule


##### What you have to know:

- The derivatives of all known functions (If not, check this lesson)
- Recognize all the basic functions
- You must be able to manipulate exponential expressions. (If not, check this lesson)
- You must be able to manipulate logarithmic expressions. (If not, check this lesson)

##### Key Points

- 1. Watch the video:
- 2. Check out this presentation .
- 3. Watch this video .

#### IB questions on differentiation


##### What you have to know:

- The derivatives of all known functions (If not, check this lesson)
- Recognize all the basic functions
- You must be able to manipulate exponential expressions. (If not, check this lesson)
- You must be able to manipulate logarithmic expressions. (If not, check this lesson)

##### Key Points

- 1. Watch the video:
- 2. Watch this video on derivatives and tangents .

#### Extra


##### Material and references:

- Hodder Book SL(ISBN: 9781510462359) : 20A, 20B, 20C

##### Key Points

- You should know how to use the chain rule to differentiate composite functions. If \( y = f(u) \), where \( u = g(x) \), then \[ \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}. \]
- You should know how to differentiate products and quotients. If \( y = u(x)v(x) \), then \[ \frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}. \] If \( y = \frac{u(x)}{v(x)} \), then \[ \frac{dy}{dx} = \frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}. \]

### IB Past Paper Problems

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