ratio of the rate of change= | Δf(x) ------ Δx |
(equation 1) |
ratio of the rate of change= | f(x + h) - f(x) ---------------- h |
(equation 2) |
lim _{h-->0} | f(x + h) - f(x) ---------------- h |
lim _{h-->0} | (x + h)^{2} - x^{2} ---------------- h |
lim _{h-->0} | x^{2} +2xh +h^{2} - x^{2} ---------------- h |
lim _{h-->0} | 2xh +h^{2} -------- h |
lim _{h-->0} | 2xh/h +h^{2}/h |
f '(x)= |
df(x) ---- dx |
(equation 3) |
d ax+b -------- dx |
= a |
d ax^{n} ------ dx |
= an x^{n-1} |
f(x) = |
g(x) ---- h(x) |
g '(x)h(x) - g(x)h '(x) ---------------------- (h(x))^{2} |
f "(x)= | d^{2} f(x) ------ dx^{2} |