class: center, middle, inverse, title-slide # Power rule (part 2) ## Differential Calculus ### Arturo Sánchez González ### <a href="mailto:arturo.sanchez@upaep.mx" class="email">arturo.sanchez@upaep.mx</a> ### April 2021 --- # Warm-up <br/> <br/> Find the derivative of the following functions: - `\(f(x) = x^{15}\)` - `\(g(x) = x^{27}\)` - `\(h(t) = t^{16}\)` --- # Non-integer powers .pull-left[ <br/> - <span style="font-size:30px"> What is the derivative of `\(y=f(x) = x^{2.34}\)`? <span/> <br/> <br/> - <span style="font-size:30px"> What is the derivative of `\(s(t) = t^{1/3}\)`? <span/> ] .pull-right[ <span style="font-size:30px"><span style="color:red"> Power rule <span/><span/> <br/> If `\(f(x) = x^{n}\)`, then <br/> <span style="color:blue"><span style="font-size:35px">$$\frac{df}{dx}(x) = n x^{n-1}$$ <span/><span/> ] --- # Negative powers <br/> - <span style="font-size:30px"> What is the derivative of `\(f(x) = \frac{1}{x}\)`? <span/> <br/> <br/> <br/> - <span style="font-size:30px"> What is the derivative of `\(g(x) = \frac{1}{x^{4}}\)`? <span/> --- # Final sprint <br/> - <span style="font-size:35px"> What is the derivative of `\(f(x) = \sqrt[4]{x^{3}}\)`? <span/> <br/> <br/> <br/> <br/> <br/> - <span style="font-size:35px"> What is the derivative of `\(s(t) = \frac{1}{\sqrt[3]{t^{2}}}\)`? <span/>