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Matérias
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Recursos > the derivative

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Instantaneous Rate of Change

"The instantaneous rate of change is the rate of change of a function at a certain time. If given the function values before, during, and after the required time, the instantaneous rate of change can ...

Important Limits

"An important limit in calculus, which is central to finding derivatives of exponential functions, involves finding the limit as h approaches 0 of a special function. This limit, one of a few importan ...

The Derivative Function

"By definition, the derivative is a function which is derived from another function. The definition of the derivative is usually only written for one point, but the function is defined for all points. ...

Derivatives of Logarithmic Functions

"The derivative of the natural logarithmic function (ln[x]) is simply 1 divided by x. This derivative can be found using both the definition of the derivative and a calculator. Derivatives of logarith ...

Derivatives of Exponential Functions

"The derivative of an exponential function can be derived using the definition of the derivative. Derivatives of exponential functions involve the natural logarithm function, which itself is an impor ...

Derivative Notation

"The two commonly used ways of writing the derivative are Newton's notation and Liebniz's notation. Newton's notation involves a prime after the function to be derived, while Liebniz's notation utiliz ...

Derivative Definition

"The definition of the derivative is the slope of a line that lies tangent to the curve at the specific point. The limit of the instantaneous rate of change of the function as the time between measure ...

Power Function Derivative

"The derivative of a power function involving x to the nth power (n being non-zero) can be derived using the definition of the derivative. The power function derivative is equal to x to the (n-1)th po ...

Polynomial Derivatives

"The derivative of a polynomial function involving multiple linear and/or power functions can be found using the formulas for finding linear and power functions, along with the constant multiple and s ...

Average Rate of Change

"The average rate of change of a population is the total change divided by the time taken for that change to occur. The average rate of change can be calculated with only the times and populations at ...

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