Question

what is the use of differentiation in mathematics

Answer 1

Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. ... Differentiation is about rates of change; for geometric curves and figures, this means determining the slope, or tangent, along a given direction.

Answer 2

We can use differentiation to determine if a function is increasing or decreasing: A function is increasing if its derivative is always positive. A function is decreasing if its derivative is always negative. y = -x has derivative -1 which is always negative and so -x is decreasing.