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Derivatives in calculus represent the rate of change of a function at a specific point. They provide information about how the function is changing at that point.
The derivative of a function f(x) at a point x=a is denoted by f'(a) or dy/dx evaluated at x=a. It is defined as the limit of the average rate of change of the function as the interval around a point approaches zero. Mathematically, the derivative is given by:
f'(a) = lim(h->0) [f(a+h) - f(a)] / h
This formula calculates the slope of the tangent line to the curve of the function at the point a. The derivative gives us information about the steepness of the curve, whether it is increasing or decreasing, and how fast it is changing.
There are different rules and techniques for finding derivatives of various types of functions, such as power functions, trigonometric functions, exponential functions, and logarithmic functions. Some common rules for finding derivatives include the power rule, product rule, quotient rule, chain rule, and trigonometric derivatives.
Derivatives in calculus represent the rate of change of a function at a specific point.
The derivative of a function f(x) at a point x=a is denoted by f'(a) or dy/dx evaluated at x=a. It is defined as the limit of the average rate of change of the function as the interval around a point approaches zero. Mathematically, the derivative is given by:
f'(a) = lim(h->0) [f(a+h) - f(a)] / h
This formula calculates the slope of the tangent line to the curve of the function at the point a. The derivative gives us information about the steepness of the curve, whether it is increasing or decreasing, and how fast it is changing.
