# Related formulas

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## Basic Derivatives

The derivative of a function multiplied by a constant ($[c]$) is equal to the constant times the derivative of the function

$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Derivative of the linear function

The derivative of the linear function is equal to $1$

$\frac{d}{dx}\left(x\right)=1$

## Derivatives of trigonometric functions

The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if ${f(x) = tan(x)}$, then ${f'(x) = sec^2(x)\cdot D_x(x)}$

$\frac{d}{dx}\left(\tan\left(x\right)\right)=\sec\left(x\right)^2\frac{d}{dx}\left(x\right)$

### Problem Analysis

$\lim_{x\to0}\left(\frac{5x}{\tan\left(x\right)}\right)$

Limits

~ 0.03 seconds