Parametric Equations Differentiation

►Refer to Khan academy: Parametric equations differentiation ►Jump over to have some practice at Khan academy.

Why can we operate dy/dx algebraically?

Refer to Khan academy: Addressing treating differentials algebraically

Jump back to previous note: How to understand dy/dx

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Differentiate Parametric Equations

▼How to take derivative of a parametric differential equation?

Example

Solve:

• Let's do some trick to dy/dt and use this one instead:

  
• Substitute the derivatives back:

  
• Plug in t=1 to get the answer:

  

Second derivatives of Parametric functions

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Example

Solve:

• Follow the rule, we got the first derivative:

  
• And let's apply the rule for second derivative: