Question

题目如下图 隐函数求导

求 详细过程

Answer 1

解：∵(x²+2y)³=2xy²+64
==>3(x²+2y)²(2x+y')=2(y²+2xyy') (等式两端对x求导数)
==>6x(x²+2y)²+3(x²+2y)²y'=2y²+4xyy'
==>[3(x²+2y)²-4xy]y'=2y²-6x(x²+2y)²
∴y'=[2y²-6x(x²+2y)²]/[3(x²+2y)²-4xy]

Answer 2

解：∵(x²+2y)³=2xy²+64
==>3(x²+2y)²(2x+2y')=2(y²+2xyy') (等式两端对x求导数)
==>6x(x²+2y)²+6(x²+2y)²y'=2y²+4xyy'
==>[6(x²+2y)²-4xy]y'=2y²-6x(x²+2y)²
∴y'=[2y²-6x(x²+2y)²]/[6(x²+2y)²-4xy]
=[y²-3x(x²+2y)²]/[3(x²+2y)²-2xy]