dy/dx
F(x)~=~f(a) +f`(a)(x-a)
The notation dy/dx is a way to represent the derivative of a function ‘y’ with respect to the variable ‘x’. It is read as the derivative of y with respect to x. Geometrically, the derivative represents the slope of the tangent line to a curve at a given point.
To find the derivative of a function, we use differentiation techniques such as the power rule, product rule, quotient rule, and chain rule. These rules allow us to find the derivative of more complex functions by breaking them down into simpler parts.
For example, consider the function y = x² + 3x. To find dy/dx, we can use the power rule and the sum rule of differentiation as follows:
dy/dx = d/dx(x²) + d/dx(3x)
= 2x + 3
Therefore, the derivative of y with respect to x is 2x + 3.
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