# expand_derivatives
展示已求导表达式
函数库: TySymbolicMath
# 语法
expand_derivatives(O,simplify)
# 说明
D = Differential(x) 表示定义一个函数 D，函数的作用是对 x 求导，expand_derivatives 展示求导表达式。示例
# 示例
求一阶导数
创建符号变量及表达式。
using TySymbolicMath
@variables x y z
f = 2*y*z*sin(x) + 3*x*sin(z)*cos(y)
f = 3x*cos(y)*sin(z) + 2y*z*sin(x)
定义三个函数，分别对 x y z 求导。
Dx = Differential(x)
Dy = Differential(y)
Dz = Differential(z)
(::Differential) (generic function with 3 methods)
将函数分别作用于表达式 f。
dx = Dx(f)
dy = Dy(f)
dz = Dz(f)
dx = Differential(x)(3x*cos(y)*sin(z) + 2y*z*sin(x))
dy = Differential(y)(3x*cos(y)*sin(z) + 2y*z*sin(x))
dz = Differential(z)(3x*cos(y)*sin(z) + 2y*z*sin(x))
利用 expand_derivatives 函数展示导数结果。
a = expand_derivatives(dx)
b = expand_derivatives(dy)
c = expand_derivatives(dz)
a = 3cos(y)*sin(z) + 2y*z*cos(x)
b = 2z*sin(x) - 3x*sin(z)*sin(y)
c = 2y*sin(x) + 3x*cos(y)*cos(z)
求十阶导数
定义表达式，并定义对 x 求十阶导函数。
using TySymbolicMath
@variables x
f = -(sin(x))^2
g = Differential(x)^10
f = -(sin(x)^2)
g = Differential(x) ∘ (Differential(x) ∘ (Differential(x) ∘ (Differential(x) ∘ (Differential(x) ∘ (Differential(x) ∘ (Differential(x) ∘ (Differential(x) ∘ (Differential(x) ∘ Differential(x)))))))))
对 f 求十阶导数。
df = g(f)
df = Differential(x)(Differential(x)(Differential(x)(Differential(x)(Differential(x)(Differential(x)(Differential(x)(Differential(x)(Differential(x)(Differential(x)(-(sin(x)^2)))))))))))
使用 expand_derivatives 函数展示导数结果。
expand_derivatives(df)
ans = 512(sin(x)^2) - 512(cos(x)^2)
# 输入参数
O - 求导表达式
由 Differential(x) 定义的对 x 求导的方法，并对表达式进行求导后，需要使用 expand_derivatives 化简展示结果。
simplify - 是否化简结果Bool（默认为 false）
表示是否化简结果表达式，非关键字参数。
示例： expand_derivatives(dx,true)