Mathematics (AS)·Differentiation · NSSCAS 2.4.3

Parametric & implicit differentiation

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In this lesson you'll learn two clever ways to find dy by dx when a curve is not written simply as y equals something. You'll differentiate parametric equations, where x and y each come from a parameter t, using dy/dx = (dy/dt)/(dx/dt). You'll differentiate implicit equations, where x and y are tangled together, remembering the all-important dy/dx factor and the product rule. You'll find gradients at given points, locate horizontal tangents, and write the equation of a tangent line.

What you'll learn in this lesson

By the end you should be able to (NSSCAS Mathematics (AS) 2.4.3):

  • Find and use the first derivative of a function which is defined parametrically.
  • Find and use the first derivative of a function which is defined implicitly.
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Parametric & implicit differentiation · NSSCAS Mathematics (AS) · namstudy