Derivative of a function
The rate of change of a function; slope of the tangent line
The derivative of a function is a mathematical tool used to measure how much a function changes at any given point. In other words, it is a measure of the rate at which the function changes with respect to its input variable. It is represented by the symbol f'(x) or dy/dx, where f(x) is the function and x is the input variable.
To find the derivative of a function, you need to apply the differentiation rules. There are several differentiation rules, including the power rule, product rule, quotient rule, and chain rule, that can be used to differentiate different types of functions. These rules provide a systematic way of finding the derivative of a function, either by hand or using software like Wolfram Alpha.
The derivative can be interpreted geometrically as the slope of a tangent line to the function at a given point. It has many real-world applications in fields like physics, engineering, and economics, where it is used to study rates of change, optimization, and approximation of complex functions.
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