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Exponential Rule

"The exponential rule is a special case of the chain rule. It is useful when finding the derivative of e raised to the power of a function. The exponential rule states that this derivative is e to the ...

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 ...

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 ...

Antidifferentiation

"Finding the antiderivatives of a function require a little backwards thinking. Since the derivative of the wanted antiderivative is the given function, checking for correctness is easy. You just take ...

Logarithm Rule

"The logarithm rule is a special case of the chain rule. It is useful when finding the derivative of the natural logarithm of a function. The logarithm rule states that this derivative is 1 divided by ...

Linear Function Derivative

"The derivative of a linear function mx + b can be derived using the definition of the derivative. The linear function derivative is a constant, and is equal to the slope of the linear function. Linea ...

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