Why Does the Chain Rule Apply Differently to the Derivative of (x^2+x)^(1/2)?

Thread starter nameVoid
Start date Mar 30, 2009
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Derivative

In summary, a simple derivative is a mathematical tool used to calculate the rate of change of one variable with respect to another variable. Its formula is dy/dx and it is used in various fields such as physics, economics, and engineering. It is different from a partial derivative in that it only calculates the rate of change with respect to one variable. The common rules for finding simple derivatives include the power rule, product rule, quotient rule, and chain rule.

Mar 30, 2009

nameVoid

D= (x^2+x)^(1/2)

Why does the chain rule in this case produce D' = (1/2)(x^2+x)^(-1/2) (2x+1)(x')

and not D' = (1/2)(x^2+x)^(-1/2) (2x+1)(2x')

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Mar 30, 2009

rock.freak667

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[tex]\frac{dD}{dt}=\frac{dx}{dt} \times \frac{dD}{dx}[/tex]

So like in the other thread, can you understand why now?

What is a simple derivative?

A simple derivative is a mathematical tool used to calculate the rate of change of one variable with respect to another variable. It measures how much a function changes when its input changes.

What is the formula for calculating a simple derivative?

The formula for a simple derivative is dy/dx, where dy represents the change in the output of a function and dx represents the change in the input of a function.

What are the applications of simple derivatives?

Simple derivatives are used in various fields such as physics, economics, and engineering to analyze and predict changes in quantities over time. They are also important in calculating instantaneous rates of change and optimizing functions.

How is a simple derivative different from a partial derivative?

A simple derivative calculates the rate of change of a function with respect to one variable, while a partial derivative calculates the rate of change of a function with respect to multiple variables. A simple derivative is a special case of a partial derivative when there is only one independent variable.

What are the common rules for finding simple derivatives?

The common rules for finding simple derivatives include the power rule, product rule, quotient rule, and chain rule. These rules allow us to find the derivative of more complex functions by breaking them down into simpler parts.