# Further Maths - Derivatives Cheat Sheet

> Source: https://ollybritton.com/notes/a-level/further-maths/topics/derivatives-cheat-sheet/ · Updated: 2022-05-19 · Tags: further-maths, a-level, school

## Flashcards
### 2022-05-19
#### Standard Trig
##### What is the derivative of $$\tan(x)$$??
$$
\sec^2(x)
$$

##### What is the derivative of $$\cot(x)$$??
$$
-\csc^2(x)
$$

##### What is the derivative of $$\sec(x)$$??
$$
\sec(x)\tan(x)
$$

##### What is the derivative of $$\csc(x)$$??
$$
-\csc(x)\cot(x)
$$

##### $$\frac{\text{d}^2}{\text{d}x^2} \sec(x) = \frac{\text{d}}{\text{d}x} \sec(x)\tan(x) = ???$$ What is the second derivative here??
$$
\sec(x)(\tan^2(x) + \sec^2(x))
$$

##### $$\frac{\text{d}^2}{\text{d}x^2} \csc(x) = \frac{\text{d}}{\text{d}x} -\csc(x)\cot(x) = ???$$ What is the second derivative here??
$$
\csc(x)(\tan^2(x) + \csc^2(x))
$$

#### Hyperbolic Trig
##### What is the derivative of $$\tanh(x)$$??
$$
\sech^2(x)
$$

##### What is the derivative of $$\sech(x)$$??
$$
-\sech(x)\tanh(x)
$$

##### What is the derivative of $$\csch(x)$$??
$$
-\csch(x)\coth(x)
$$

##### What is the derivative of $$\coth(x)$$??
$$
-\csch^2(x)
$$

##### $$\frac{\text{d}^2}{\text{d}x^2} \sech(x) = \frac{\text{d}}{\text{d}x} -\sech(x)\tanh(x) = ???$$ What is the second derivative here??
$$
\sech(x)(\tanh^2(x) - \sech^2(x))
$$

##### $$\frac{\text{d}^2}{\text{d}x^2} \csch(x) = \frac{\text{d}}{\text{d}x} -\csch(x)\coth(x) = ???$$ What is the second derivative here??
$$
\csch(x)(\coth^2(x) + \csch^2(x))
$$

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