14E - Differentiation of power functions
For power functions, the derivative can be determined using the following rule:
■ If \(f(x)=ax^n\), then \(f'(x)=n \times ax^{n-1}\).
14E - Example 1: Differentiation of power functions by rule
Determine the derivative of each of the following functions.
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14E - Example 1: Video solution
14E - Example 1: Practice
Question 1: If \(f(x)=\frac{4}{x^3}\), find \(f'(x)\). Question 2: If \(y=6x^{\frac{1}{3}}\), determine \(\frac{dy}{dx}\). Question 3: Compute \(\frac{d}{dx}((\sqrt{x})^5)\). 14E - Example 1: Solutions
Question 1: \(f(x)=4x^{-3} \therefore f'(x)=-\frac{12}{x^4}\) Question 2: \(\frac{dy}{dx}=2x^{\frac{-2}{3}}=\frac{2}{\sqrt[3]{x^2}}\) Question 3: \(\frac{d}{dx}((\sqrt{x})^5)=\frac{5x^{\frac{3}{2}}}{2}=\frac{5\sqrt{x^3}}{2}\) |