1、复合函数链式求导计算一阶导数
由复合函数求导法则，对x求导有：
dy/dx=3*sin^2(14x^2+20x+56)*cos(14x^2+20x+56)*(14x^2+20x+56)’
=3*sin^2 (14x^2+20x+56)*cos(14x^2+20x+56)*(28x+20),
=3(28x+20)*sin^2 (14x^2+20x+56) *cos(14x^2+20x+56).
2、取对数求导计算一阶导数
首先对方程两边取对数，有：
lny=lnsin^3 (14x^2+20x+56),
lny=3lnsin(14x^2+20x+56),
3、方程两边同时对x求导，有：
y’/y=3 [sin(14x^2+20x+56)]’/sin(14x^2+20x+56),
y’/y=3 [cos(14x^2+20x+56)](28x+20)/sin(14x^2+20x+56),
y’=sin^3(14x^2+20x+56)*3[cos(14x^2+20x+56)](28x+20)/sin(14x^2+20x+56),
y’=sin^2 (14x^2+20x+56)*3[cos(14x^2+20x+56)](28x+20),
=3 (28x+20)sin^2 (14x^2+20x+56)*cos(14x^2+20x+56).
4、二阶导数计算
本处根据函数特征，采取取对数计算导数，
首先对函数两边同时取对数，有：
lny’=ln3(28x+20)sin^2 (14x^2+20x+56)*cos(14x^2+20x+56),则：
lny’=ln3+ln(28x+20)+2lnsin(14x^2+20x+56)+lncos(14x^2+20x+56),
对方程两边同时对x再次求导，
5、y’’/y’=28/(28x+20)+2[sin(14x^2+20x+56)]’/sin(14x^2+20x+56)+[cos(14x^2+20x+56)]’/cos(14x^2+20x+56),
=28/(28x+20)+2cos(14x^2+20x+56)(28x+20)/sin(14x^2+20x+56)-sin(14x^2+20x+56)(28x+20)/cos(14x^2+20x+56),
=28/(28x+20)+2(28x+20)ctg(14x^2+20x+56)-(28x+20)tan(14x^2+20x+56),则：
y’’=3(28x+20)sin^2(14x^2+20x+56)*cos(14x^2+20x+56)[28/(28x+20)+2(28x+20)ctg(14x^2+20x+56)-(28x+20)tan(14x^2+20x+56)],
=84sin^2(14x^2+20x+56)*cos(14x^2+20x+56)+6(28x+20)^2sin^1(14x^2+20x+56)*cos^2(14x^2+20x+56)-3(28x+20)^2sin^3(14x^2+20x+56),
=42sin^1(14x^2+20x+56)*sin(28x^2+40x+112)+6(28x+20)^2sin^1(14x^2+20x+56)*cos^2(14x^2+20x+56)-3(28x+20)^2sin^3(14x^2+20x+56)。