Definition of Derivative

If y=f(x) is a function of the variable x, then the derivative of y=f(x) at some x=a, is the rate of change of the function with respect to x at a.

The derivative is often interpreted as the slope of the graph of y=f(x) at x=a.

The derivative of y=f(x) is usually written dy/dx or f'(x).

For f(x)=x^3

f'(x)=3x^2, thus the rate of change of x^3 at x=4 is 3×4^2=48.

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