Implicit Differentiation (OCR A Level Maths A) : Revision Note

Implicit Differentiation

What is implicit differentiation?

• An equation connecting x and y is not always easy to write explicitly in the form y= f(x) or x = f(y)

• However you can still differentiate such an equation implicitly using the chain rule:

• Combining this with the product rule gives us:

• These two special cases are especially useful:

• When x and y are connected in an equation you can differentiate both sides with respect to x and rearrange to find a formula (usually in terms of x and y ) for dy/dx

  • Note that dy/dx is a single algebraic object

  • When rearranging do not treat dy/dx as a fraction

  • Especially do not try to separate dy and dx and treat them as algebraic objects on their own!