Symbolically this is the limit of fc-fchh as h0. The derivative function becomes a map between the tangent bundles of M and N. Derivative is a rate of change of function with respect to a variableAfter the invention of a derivative of a function by Newton and Leibnitz in around 17th century it is widely used in the sector of math and physics.
We can estimate the rate of change by doing the calculation of the ratio of change of the function Delta y with respect to the change of the independent variable Delta x.
Wataru Aug 29 2014 Is there a difference between lim h0 f x h f x h and lim dx0 f x dx f x dx. The derivative of function f at xc is the limit of the slope of the secant line from xc to xch as h approaches 0. Derivative Functions The derivative function gives the derivative of a function at each point in the domain of the original function for which the derivative is defined. Definition of Derivative As we saw as the change in x is made smaller and smaller the value of the quotient often called the Difference Quotient comes closer and closer to 4.