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Partial derivatives

You'll learn the concept of a partial derivative, and calculate derivatives from its mathematical definition.

Partial derivatives is a didactic content from Sangakoo. In this space you will find te ...

Velocity and Acceleration

"If position is given by a function p(x), then the velocity is the first derivative of that function, and the acceleration is the second derivative. By using differential equations with either velocit ...

Using the First Derivative Test

"Some optimization problems use the first derivative test to find an absolute minimum or maximum. Using the first derivative test requires the derivative of the function to be always negative on one s ...

Intervals of Increase and Decrease

"Finding intervals of increase and decrease of a function can be done using either a graph of the function or its derivative. These intervals of increase and decrease are important in finding critical ...

Inflection Points

"Inflection points are points on the graph where the concavity changes. A positive second derivative means a function is concave up, and a negative second derivative means the function is concave down ...

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. ...

Substitution Method

"The substitution method is a very valuable way to evaluate some indefinite integrals. The substitution method adds a new function into the one being integrated, and substitutes the new function and i ...

General Power Rule

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

First Derivative Test

"The first derivative test is a way to find if a critical point of a continuous function is a relative minimum or maximum. Simply, if the first derivative is negative to the left of the critical point ...

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