Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 3.3 : Differentiation Formulas
5. Find the derivative of \(y = \sqrt x + 8\,\sqrt[3]{x} - 2\,\sqrt[4]{x}\) .
Show SolutionThere isn’t much to do here other than take the derivative using the rules we discussed in this section.
Remember that you’ll need to convert the roots to fractional exponents before you start taking the derivative. Here is the rewritten function.
\[y = {x^{\frac{1}{2}}} + 8{x^{\frac{1}{3}}} - 2{x^{\frac{1}{4}}}\]The derivative is,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{dy}}{{dx}} = \frac{1}{2}{x^{ - \,\,\frac{1}{2}}} + \frac{8}{3}{x^{ - \,\,\frac{2}{3}}} - \frac{1}{2}{x^{ - \,\,\frac{3}{4}}}}}\]