Extending differentiation to inverse trigonometric and hyperbolic functions, implicit relations and parametric curves, plus Maclaurin series.
Syllabus points covered
- Differentiate inverse trigonometric and inverse hyperbolic functions
- Use implicit and parametric differentiation, including second derivatives
- Find and use Maclaurin series for standard functions
- Determine the nature of stationary points using higher derivatives
Common mistakes
- Finding the second derivative parametrically by differentiating dy/dx with respect to t and stopping — it must then be divided by dx/dt.
- Forgetting the chain rule factor when differentiating an inverse function of something other than x.
- Truncating a Maclaurin series before the number of terms the question asked for.
- Differentiating a y-term implicitly without attaching dy/dx.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questions
- Mark scheme
- Step-by-step worked solutionsComing soon
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