Question

隐函数求导1.x^2+y^2=492.√x+√y=103.(x-2)y^3=x+24.(x^2+y^2)^3=4x^5y

Answer 1

1.x^2+y^2=49

2x+2y*y'=0

y'=-x/y

2.√x+√y=10

1/(2√x)+1/(2√y)*y'=0

y'=-√(y/x)

3.(x-2)y^3=x+2

y^3*(x-2)+3y^2*y'=1

y'=[1-y^3*(x-2)]/(3y^2)

4.(x^2+y^2)^3=4x^5y^6

3(x^2+y^2)^2*(x^2+y^2)'=4(5x^4*y^6+6x^5*y^5*y')

3(x^2+y^2)^2*(2x+2y*y')=4(5x^4*y^6+6x^5*y^5*y')

6x(x^2+y^2)^2+6y(x^2+y^2)^2*y'=20x^4*y^6+24x^5*y^5*y'

y'=[20x^4*y^6-6x(x^2+y^2)^2]/[[6y(x^2+y^2)^2-24x^5*y^5]