Chain Rule for Higher-Order Derivatives
Consider the function . How does the application of the Chain Rule and Power Rule in finding the third derivative compare to their application in finding the first derivative?
The Chain Rule is only applied once, but the Power Rule is used three times, reducing the overall exponent from 4 to 1.
The Chain Rule becomes unnecessary after the first derivative, and only the Power Rule is applied for the second and third derivatives.
The Chain Rule is applied three times, resulting in a more complex product of the power term and the derivatives of the inner function, while the Power Rule reduces the exponent to 1 in the final step.
Both the Chain Rule and Power Rule are applied identically for each derivative, merely increasing the complexity of the resulting expression.
Question Leaderboard
Not enough data yet to show leaderboard.