6B - Differentiation of power functions
For power functions, the derivative can be determined using the following rule:
■ If \(f(x)=ax^n\), then \(f'(x)=n\times ax^{n-1}\).
6B - Example 1: Differentiation of power functions by rule
Determine the derivative of each of the following:
(a) \(f(x)=3x^2+4x+8\) (b) \(g(x)=-\frac{3}{4}x^2+5x+9\) (c) \(h(x)=x^4-\frac{3x^2}{2}+7x-10\) (d) \(y=\frac{3}{x^2}\) (e) \(y=-4\sqrt{x}\) (f) \(y=\frac{1}{x}+\frac{6}{\sqrt{x}}\) |
6B - Example 1: Video solution
6B - Example 1: Practice
Question 1: If \(f(x)=-5x^2+3x\), find \(f'(x)\). Question 2: Consider the function \(y=6\sqrt{x}\). (a) Find \(f'(x)\) (b) Evaluate \(f'(4)\) Question 3: If \(y=\frac{-4}{x^2}+6x\), find \(\frac{dy}{dx}\). 6B - Example 1: Solutions
Question 1: \(f'(x)=-10x+3\) Question 2: (a) \(f'(x)=3x^{-\frac{1}{2}}=\frac{3}{\sqrt{x}}\) (b) \(f'(4)=\frac{3}{\sqrt{4}}=\frac{3}{2}\) Question 3: \(\frac{dy}{dx}=\frac{8}{x^3}+6\) |
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Additional Exercises
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Topic Worksheets
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VCAA Questions
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Please view Topic Worksheets for any additional questions available at this point in time.
Differentiation of power functions by rule - Worksheet A
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Past VCAA examination questions have relied on these skills when applying the chain, product and quotient rules.
Other resources from external sources may be collated here in the future.
If you know of any good resources that could be included here, please send them via email.
If you know of any good resources that could be included here, please send them via email.