Topics | Description | Answer Key |
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Power Rule for Differentiation - Worksheet 1 - Exponent is a Positive Integer | Use of the power rule to differentiate functions, which can be written \(f(x)=ax^n\) where \(n\) is a positive integer, such as \(f(x) = 3x^5\), \(y = 6x^2+3\), ... . | HERE |
Power Rule for Differentiation - Worksheet 2 - Exponent is a Negative Integer | Use of the power rule to differentiate functions, which can be written \(f(x)=ax^n\) where \(n\) is a negative integer, such as \(f(x) = \frac{5}{x^2}\), \(y = 2x+\frac{3}{x^2}\), ... . | HERE |
Power Rule for Differentiation Worksheet 3 - Gradients of Curves | Given the equation of several curves, such as \(y = x+\frac{1}{x}\), exercises consist of finding \(\frac{dy}{dx}\) and calculating the gradient of the curve at a point along its length. | HERE |
Topics | Description | Answer Key |
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Finding Stationary Points - Worksheet 1 | Finding the \(x\) and \(y\) coordinates of stationary points, by solving \(\frac{dy}{dx} = 0\). The functions worked with in the worksheet can all be differentiated using the power rule for differentiation. | |
Finding Stationary Points - Worksheet 2 | Finding the \(x\) and \(y\) coordinates of stationary points, by solving \(\frac{dy}{dx} = 0\). The functions worked with in the worksheet can all be differentiated using the power rule for differentiation and are all of the form \(y = ax+\frac{b}{x}\) for instance \(y = 2x+\frac{8}{x}\). These functions are frequently seen in exam-type questions. |