Changes

===Introduction to derivative===

===Introduction to derivative===

If a function has value <math>f(x)</math> at <math>x</math> and <math>f(x+h)</math> at <math>x+h</math> with <math>h>0</math> than the gradient of the line joining <math>(x,f(x))</math> to <math>(x+h,f(x+h))</math> is,

If a function has value <math>f(x)</math> at <math>x</math> and <math>f(x+h)</math> at <math>x+h</math> with <math>h>0</math> than the slope of the line joining <math>(x,f(x))</math> to <math>(x+h,f(x+h))</math> is,

:<math>\frac{f(x+h)-f(x)}{h}</math>.

:<math>\frac{f(x+h)-f(x)}{h}</math>.

Therefor the gradient of the line that meet (is tangential to) <math>f(x)</math> at <math>x</math> is the limit as <math>h</math> tends to zero, or,

Therefor the slope of the line that meet (is tangential to) <math>f(x)</math> at <math>x</math> is the limit as <math>h</math> tends to zero, or,

:<math>\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h},</math>

:<math>\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h},</math>