class: center, middle, inverse, title-slide # Derivative rules (part 1) ## Differential Calculus ### Arturo Sánchez González ### <a href="mailto:arturo.sanchez@upaep.mx" class="email">arturo.sanchez@upaep.mx</a> ### April 2021 --- # Warm-up <span style="font-size:30px">Find the derivatives of the following functions: <span/> .pull-left[ - <span style="font-size:30px"> `\(f(x) = x^{31}\)`<span/> <br/> <br/> <br/> - <span style="font-size:30px"> `\(s(t) = t^{-3.2}\)`<span/> ] .pull-right[ - <span style="font-size:30px"> `\(g(x) = \frac{1}{x^{7}}\)`<span/> <br/> <br/> <br/> - <span style="font-size:30px"> `\(h(t) = \frac{1}{\sqrt[4]{t^{3}}}\)`<span/> ] --- # Velocity, again <span style="font-size:30px"> If a car is parked, what is its velocity at any moment? <span> <br/> <center> <img src="images/constant.png"> <center/> --- # Derivative of constant functions <br/> <br/> <span style="font-size:30px"> Let `\(c\)` be a number. Consider `\(f(x) = c\)`, then <span/> <br/> <br/> <span style="font-size:40px">$$f'(x) = \frac{df}{dx}(x) = 0$$ <span/> --- # Examples <span style="font-size:30px">Find the derivatives of the following functions <span/> .pull-left[ <br/> - <span style="font-size:30px"> `\(f(x) = 10^{6}\)` <span/> <br/> <br/> <br/> - <span style="font-size:30px"> `\(g(t) = 456\)` <span/> ] .pull-right[ <br/> - <span style="font-size:30px"> `\(h(x) = 9876543\)` <span/> <br/> <br/> <br/> - <span style="font-size:30px"> `\(\ell(t) = 765^{123}\)` ]