Changes

For a real-valued function <math>f(x)</math> of one variable, the derivative of <math>f</math> corresponds to the [[slope]] of the tangent line to the graph of ''f'' at ''x''.

For a real-valued function <math>f(x)</math> of one variable, the derivative of <math>f</math> corresponds to the [[slope]] of the tangent line to the graph of ''f'' at ''x''.

The roots of differentiation are profoundly linked with tangency ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].\cite

The roots of differentiation are profoundly linked with tangency ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].

When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over <math>[x,x+h]</math> as <math>h</math> tends to zero. In other words, the derivative

When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over the interval <math>[x,x+h]</math> as <math>h</math> tends to zero. In other words, the derivative

:<math>f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}</math>

:<math>f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}</math>