Derivative of transcendental functions

class: center, middle, inverse, title-slide

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

---

# Warming up

Find the derivative of the following functions.

.pull-left[

- `$f(t) = -3t -25^{87}$`

- `$g(x) = 2x^{3}-7x^{5}$`
]

.pull-right[

- `$h(x) = 3\sqrt[9]{x^{5}} - 6$`

- `$s(t)= \frac{4}{t^{6}} - 3t^{10}$`
]

---

# Trigonometric functions: sine

---

# Trigonometric functions: cosine

# Derivatives of trigonometric functions

If `$f(x) = \sin(x)$`, then

$$\frac{df}{dx}(x) = f'(x) = \cos (x)$$

If `$g(x) = \cos (x)$`, then

$$\frac{dg}{dx}(x) = g'(x) = -\sin (x)$$

---

# Exponential function

---

# Derivative of exponential function

If `$f(x) = e^{x} = \exp (x)$`, then

$$\frac{df}{dx}(x) = f'(x) = e^{x}$$

---

# Logarithmic function

---

# Derivative of logarithmic function

If `$f(x)=\ln (x)$`, then

`$$\frac{df}{dx}(x) = f'(x) = \frac{1}{x}$$`

---

# Stretching out

.pull-left[
- `$h(x) = \sin (x) + e^{x}$`

- `$s(t)= \cos (t) - \ln (t)$`
]

.pull-right[
- `$f(t)=-16\sin (t)$`

- `$r(x) = x^{6} + 3\sin(x)$`
]

---

#References

- For the sinus function
 + Castillo, J. (2013, November 4). Derivada de función seno. GeoGebra. https://www.geogebra.org/m/x8b6cduc.

- For the cosine function
  + Castillo, J. (2013, November 4). Derivada de función coseno. GeoGebra. https://www.geogebra.org/m/DqKZbpY9.

- For the exponential function
 + Fúneme, C. (2017, March 21). DERIVADA EXPONENCIAL. GeoGebra. https://www.geogebra.org/m/HTe3PMn6.

- For the logarithmic function
 + Sánchez, A. (2021, May 6). Derivative of logarithmic function. GeoGebra. https://www.geogebra.org/m/k2xujegw.