Derivative of y
The derivative of a function y with respect to a variable x is a measure of how the function y changes as the variable x changes
The derivative of a function y with respect to a variable x is a measure of how the function y changes as the variable x changes. Mathematically, it represents the rate of change or the slope of the function at a particular point.
The derivative of y with respect to x is denoted as dy/dx, or f'(x), where f(x) represents the function y.
To find the derivative of a function, you can use various techniques, including the Power Rule, Product Rule, Quotient Rule, and Chain Rule, depending on the complexity of the function.
For example, if y = x^2, we can find the derivative dy/dx as follows:
Using the Power Rule, we bring down the exponent and multiply it by the coefficient:
dy/dx = 2x.
This means that for any value of x, the rate of change of the function y = x^2 is given by 2x. For example, when x = 3, the derivative dy/dx = 2(3) = 6, indicating that at that particular point, the function is changing at a rate of 6 units per unit change in x.
Derivatives have many applications in mathematics and various fields, including physics, engineering, economics, and computer science, where they are used to analyze rates of change, optimization, and finding tangent lines to curves.
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