Product rule (part 2)

class: center, middle, inverse, title-slide

# Product rule (part 2)
## 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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# Product rule (again)

If `$f(x)$` `$=$` `$g(x)$` `$\cdot$` `$h(x)$` , then

<center>

 `$\frac{df}{dx}(x)$` `$=$` `$g(x)$` `$\cdot$` `$\frac{dh}{dx}(x)$` `$+$` `$h(x)$` `$\cdot$` `$\frac{dg}{dx}(x)$`

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# Review of last exercise

Find the derivative of the following function

`$$h(x) = 5\cos (x) + x^{4}\ln (x) +2 - e^{x}\cos(x)$$`

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# More examples (1/2)

Find the derivative of the following function

`$$s(t) = -5\cos (t) \ln(t) + 4te^{t}$$`

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# More examples (2/2)

Find the derivative of the following function

`$$v(x) = -x^{4}\sin (x) + \sin (x)\cos (x)$$`

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# Stretching out

Find the derivatives of the following functions.

.pull-left[
- `$r(x) = -27^{9}x + 36$`

- `$m(t) = -\frac{1}{15}t^{15} + \ln (t)$`
]

.pull-right[
- `$g(t) = 10\sin(t) - 5e^{t}$`

- `$\ell (x) = 0$`
]