百度作业网复合函数的导数方程求法?
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/04/24 19:03:20
复合函数的导数方程求法?
A=F(Z)
Z=G(Y)
Y=H(X)
求：dA/dX=?
dA/dX=(dA/dZ)(dZ/dY)(dY/dX)
dA/dX = (dF/dZ)(dG/dY)(dH/dX)
举例：F(Z)=Z^2 G(Y)=SINY H(X)=LN X
那么：dA/dX = 2Z*COSY/X
= 2G(Y)COS[H(X)]/X
= 2G[H(X)]COS[H(X)]/X
= 2SIN[H(X)]COS[LN X]/X
= 2SIN(LN X)COS(LN X)/X
= SIN(2LN X)/X
实际上：A=F{G[H(X)]}=F{G[ln X]}=G^2(ln X)=SIN^2(lnX)
dA/dX=2SIN(lnX)COS(lnX)/X
Z=G(Y)
Y=H(X)
求：dA/dX=?
dA/dX=(dA/dZ)(dZ/dY)(dY/dX)
dA/dX = (dF/dZ)(dG/dY)(dH/dX)
举例：F(Z)=Z^2 G(Y)=SINY H(X)=LN X
那么：dA/dX = 2Z*COSY/X
= 2G(Y)COS[H(X)]/X
= 2G[H(X)]COS[H(X)]/X
= 2SIN[H(X)]COS[LN X]/X
= 2SIN(LN X)COS(LN X)/X
= SIN(2LN X)/X
实际上：A=F{G[H(X)]}=F{G[ln X]}=G^2(ln X)=SIN^2(lnX)
dA/dX=2SIN(lnX)COS(lnX)/X