Question

Finding Derivatives Implicity In Exercise, find dy/dx implicity.
x2 - 3 ln y + y2 = 10

Answer 1

`(dy)/(dx)=-(2xy)/(2y^2-3)`

Explanation:

We are given that

`x^2-3lny+y^2=0`

Differentiate w.r.t x

`2x-(3)/(y)(dy)/(dx)+2y(dy)/(dx)=0`

By using formula

`(dx^n)/(dx)=nx^(n-1)`

`(d(lnx))/(dx)=(1)/(x)`

`(dy^n)/(dx)=ny^(n-1)(dy)/(dx)`

`(dy)/(dx)(-(3)/(y)+2y)+2x=0`

`(dy)/(dx)(-(3)/(y)+2y)=-2x`

`(dy)/(dx)=-(2x)/(-(3)/(y)+2y)`

`(dy)/(dx)=-(2xy)/(2y^2-3)`

Hence, the derivative of function

`(dy)/(dx)=-(2xy)/(2y^2-3)`