dy/dx
The symbol “dy/dx” represents the derivative of the dependent variable y with respect to the independent variable x
The symbol “dy/dx” represents the derivative of the dependent variable y with respect to the independent variable x. In other words, it represents the rate of change of y with respect to x. The derivative measures how a function (in this case, y) changes as its input (x) changes.
To calculate dy/dx, you would typically apply the rules of differentiation. The most common method is to use the power rule, which states that if y = x^n, where n is a constant, then dy/dx = nx^(n-1).
For example, let’s say we have the function y = 3x^2. Applying the power rule, we find that dy/dx = 6x^(2-1) = 6x. This means that the rate of change of y with respect to x is 6 times the value of x.
It’s important to note that dy/dx can also be interpreted geometrically as the slope of a tangent line to the graph of the function y = f(x) at a given point (x, y). The derivative provides information about the steepness or slope of the function at a specific point. If dy/dx is positive, it indicates that y is increasing as x increases, whereas if dy/dx is negative, it shows that y is decreasing as x increases.
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