Chain rule (part 2)

class: center, middle, inverse, title-slide

# Chain rule (part 2)
## Differential Calculus
### Arturo Sánchez González
### <a href="mailto:arturo.sanchez@upaep.mx" class="email">arturo.sanchez@upaep.mx</a>
### May 2021

---

# Chain rule

Let `$\color{red}{g(x)}$` and `$\color{blue}{h(x)}$` be two functions. Then `$\color{green}{f(x)} = \color{red}{g}\left( \color{blue}{h(x)} \right)$` is also a function and

`$$\color{darkgreen}{f'(x)} = \color{darkred}{g'}\left( \color{blue}{h(x)}\right) \cdot \color{darkblue}{h'(x)}$$`

---

#More examples (1/2)

Find the derivative of the following function

`$$\color{green}{r(x) = \left(3\cos (x) + 28 - \ln(x)\right)^5}$$`

---
#More examples (2/2)

Find the derivative of the following function

`$$\color{green}{f(t) = e^{\left(\frac{6-7t}{5}\right)}}$$`

---

# Dig deeper (1/2)

Find the derivative of the following function

`$$\color{green}{s(x) = \frac{4\cos\left(-7e^{x} -\ln(x) \right)}{7}}$$`

---

# Dig deeper (2/2)

Find the derivative of the following function

`$$\color{green}{v(t) = -\frac{2}{3}\ln\left(\frac{1}{t} \right)}$$`