# Calculus 1 - A Khan academy revision guide

(under construction ... abandoned until I have students who need this)

We summarise the most important skills in ... and link to the corresponding exercises in Khan academy. For a complete course on the subject see ... For examples see Khan or Wikipedia, we only list the essentials.

## Derivatives

We need to know the following formulas to compute basic derivatives:

$$(e^x)' = e^x
\quad\quad\quad\quad
(ln x)' = 1/x
$$

$$ sin(x)' = cos(x)
\quad\quad\quad\quad
cos(x)' = - sin(x)
$$

$$(x^n)' = n x^{n-1}$$

And the following rules that allow us to compute more complicated derivatives from simpler ones:

...

Using the Cheat-Sheet above, it is possible to solve all of the following Exercises:

[Differentiate polynomials](https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6b/e/power-rule-basic)

[Tangents of polynomials](https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6b/e/tangents-of-polynomials)

...

## Implicit differentiation

## L'Hospital

## Integration

## Substitution rule