Derivative of polynomial functions

# Derivative of polynomial functions
## Differential Calculus
### Arturo Sánchez González
### <a href="mailto:arturo.sanchez@upaep.mx" class="email">arturo.sanchez@upaep.mx</a>
### May 2021

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# Power rule

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# Quick review

Find the derivative of the following functions.

- `$g(t) = -\frac{5}{3t^{9}}$` 
]

- `$v(x)=\frac{2}{865^{17}}$` 
]

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# Derivative of the sum of functions

Let `$f(x)$` and `$g(x)$` be functions.

Then, the derivative of `$f(x) + g(x)$` is

`$$\begin{matrix}\frac{d}{dx} \left[ f(x) + g(x)\right] & = & \frac{d}{dx}\left[ f(x)\right] + \frac{d}{dx}\left[ g(x)\right] \\ \\ & = & f'(x) + g'(x)\end{matrix}$$`

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# First examples (1/2)

Find the derivative of `$f(x) = 4x^{2} + 5$`.

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# First examples (2/2)

Find the derivative of `$s(x) = 9+ 3x^{2} + 5x$`.

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# You vs internet

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# Dig deeper

Find the derivative of the following function

`$$f(x) = 3x^{4} + 8x^{3} - 7x^{2} + 12x -10^{6}$$`

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# Stretching out

Find the derivative of the following function

`$$s(x) = -\frac{3}{x^{4}} + 5 - 3x$$`