Sum rule

class: center, middle, inverse, title-slide

# Sum rule
## 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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# Warming up

Find the derivative of the following functions.

.pull-left[
- `$f(x) = 6x^{4}$`

- `$g(t) = 25 + 10^{6}$`
]

.pull-right[
 `$h(t) = \frac{1}{t^{5}} + t^{3}$`

`$\ell (x) = 4\sqrt[8]{x^{6}}$`
]

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# Derivatives of polynomial functions (1)

Find the derivative of the following function.

`$$s(x) = -5x^{6}+3x^{2}-23x-10^{-100}$$`

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# Derivatives of polynomial functions (2)

Find the derivative of the following function.

`$$v(t) = 7t^{6} - \frac{2}{3}t^{4} - \frac{5}{6}t^{3} + t - 20$$`

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# Dig deeper

Find the derivative of the following function.

`$$m(x) = \frac{2}{5}\sqrt[3]{x^{2}} + 4x - \frac{3}{x^{4}}$$`

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# Stretching out

Find the derivative of the following function.

.pull-left[
- `$r(x) = -125$`

- `$f(x) = \frac{3}{x^{4}}$`
]

.pull-right[
- `$g(t)= \frac{1}{\sqrt[6]{t^{5}}}$`
]