Definition of Derivatives 1st Derivative The derivative of a function describes how changes in one variable are related to changes in another. One representation of this concept in geometry is in the slope of the tangent to a curve. The derivative of a function y = f(x) is defined as:     2nd Derivative If y = f(x) is a differentiable function, then differentiation produces a new function y' = f'(x) called the first derivative of y with respect to x. If y' = f'(x) is in turn a differentiable function, then its derivative, df'(x)/dx, is called the second derivative of y with respect to x.     3rd Derivative Likewise, the third derivative is the derivative of the second derivative.     General Form In general, the nth derivative of f is denoted by f (n) and is obtained from f by differentiating n times, as such:

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