class: center, middle, inverse, title-slide # Quotient rule (part 2) ## Differential Calculus ### Arturo Sánchez González ### <a href="mailto:arturo.sanchez@upaep.mx" class="email">arturo.sanchez@upaep.mx</a> ### May 2021 --- # Quotient rule </br> <span style="font-size:35px"> If `\(\color{green}{f(x)} = \frac{\color{red}{g(x)}}{\color{blue}{h(x)}}\)`, then </span> </br> </br> <span style="font-size:40px"> `$$\color{green}{\frac{df}{dx}(x)} = \frac{ \color{blue}{h(x)} \cdot \color{darkred}{g'(x)} - \color{red}{g(x)} \cdot \color{darkblue}{h'(x)} }{ \left(\color{blue}{h(x)}\right)^2 }$$` </span> --- # Let's practice! (1/2) <span style="font-size:30px"> Find the derivative of the following function. </span> <span style="font-size:35px;color:darkgreen">$$s(t) = \frac{3t^2}{\ln (t)}$$ --- # Let's practice! (2/2) <span style="font-size:30px"> Find the derivative of the following function. </span> <span style="font-size:35px;color:darkgreen">$$r(x) = \frac{3x^5 - \cos (x)}{e^{x}}$$ --- # Dig deeper <span style="font-size:30px"> Find the derivative of the following function. </span> <span style="font-size:35px;color:darkred">$$v(t) = \frac{4t^5 + 506 - \cos(t)}{ \sin (t) + \frac{2 \ln (t)}{3}}$$