# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-calculus-Derivatives%20of%20known%20functions.html


## Derivatives

"But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not" Johann Bernoulli


#### Derivatives of known Functions


##### What you have to know:

- Recognize all the basic functions
- You must be able to expand and factorise the square difference and perfect square expressions. (If not, check this lesson)
- 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 .

#### Geometric explanation of Derivatives


##### What you have to know:

- How to calculate Area

##### Key Points

- 1. Watch the video:

#### Extra


##### Material and references:

- Hodder Book SL(ISBN: 9781510462359) : 9A, 9B, 9C, 20A

##### Key Points

- You should be able to differentiate functions such as \( \sqrt{x} \), \( \sin x \) and \( \ln x \). If \( f(x) = x^n \), where \( n \in \mathbb{Q} \), then \( f'(x) = nx^{n-1} \); if \( f(x) = \sin x \), then \( f'(x) = \cos x \); if \( f(x) = \cos x \), then \( f'(x) = -\sin x \); if \( f(x) = e^x \), then \( f'(x) = e^x \); and if \( f(x) = \ln x \), then \( f'(x) = \frac{1}{x} \).

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