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Differential Equations

"Differential equations are equations with a derivative of an unknown function. Solving a differential equation requires using antidifferentiation. Since they use antiderivatives, there are multiple s ...

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 ...

Quotient Rule

"The quotient rule is useful when trying to find the derivative of a function that is divided by another function. As long as both functions have derivatives, the quotient rule tells us that the final ...

Critical Points

"Critical points are places where the derivative of a function is either zero or undefined. These critical points are places on the graph where the slope of the function is zero. All relative maxima a ...

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 ...

Closed Interval Method

"The closed interval method is a way to solve a problem within a specific interval of a function. The solutions found by the closed interval method will be at the absolute maximum or minimum points on ...

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