Nth derivative of algebraic function

In summary, the Nth derivative of an algebraic function is the derivative of the function taken N times, calculated using the power rule of differentiation. It provides information about the function's behavior and can be negative if the function is decreasing at that point. Other methods, such as the quotient rule and chain rule, can also be used to calculate the Nth derivative, but the power rule is the most commonly used method.
  • #1
anil86
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Find nth derivative of following algebraic function:

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  • #2
Nice approach! I would try plugging in specific values of $x$. The $A,B,C$ relation you have found must hold for all $x$, so it should hold for, say, $x=1$ and $x=-3/2$. Then I would just pick another nice value for $x$, say, $x=0$. You get three equations in three unknowns, technically, but I don't think it'll end up being that complicated.
 

FAQ: Nth derivative of algebraic function

What is the definition of "Nth derivative of algebraic function"?

The Nth derivative of an algebraic function is the derivative of the function taken N times. It represents the rate of change of the function at a given point and can be calculated using the power rule of differentiation.

How is the Nth derivative of an algebraic function calculated?

The Nth derivative of an algebraic function can be calculated using the power rule of differentiation, where the coefficient of the variable is multiplied by the exponent and then the exponent is decreased by 1. This process is repeated N times.

What is the significance of the Nth derivative of an algebraic function?

The Nth derivative of an algebraic function can provide information about the behavior of the function at a specific point. It can also help determine the concavity and inflection points of the function.

Can the Nth derivative of an algebraic function be negative?

Yes, the Nth derivative of an algebraic function can be negative if the function is decreasing at that specific point. This indicates that the function is decreasing at an increasing rate.

Are there any other methods to calculate the Nth derivative of an algebraic function?

Yes, there are other methods such as the quotient rule, product rule, and chain rule that can be used to calculate the Nth derivative of an algebraic function. However, the power rule is the most commonly used method.

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