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The Implicit differentiation exercise appears under the Differential calculus Math Mission on Khan Academy. This exercise solves derivatives in equation form that have multiple variables.

Types of Problems Edit

There are three types of problems in this exercise:

  1. Find the derivative of the function: The student is asked to find the derivative of a function that has multiple variables.
    Implicit diff1

    Find the derivative of the function

  2. Find the rate in which values are changing: The student is asked to find the rate of change of two variables from the function.
  3. Find the slope of the tangent: The student is asked to find the slope of the tangent line at a particular point.

Strategies Edit

Knowledge basic derivative concepts are encouraged to ensure success on this exercise.

  1. The equation of a unit circle is and it's derivative is x^2+y^2=1 and it's derivative is -x/y
  2. Implicit diff2

    Find the slope of the tangent line

    The derivative of is xsqrt(y)=1 is -2x^{-3}
  3. The derivative of is e^{xy^2}=x-y is  \frac{1-y^2e^{xy^2}}{2xye^{xy^2}+1}
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