Question

Finding Derivatives Implicity In Exercise, find dy/dx implicity.
4x3 + ln y2 + 2y = 2x

Answer 1

`(dy)/(dx)=(y(1-6x^2))/((1+y))`

Explanation:

Given function : 4x³ + ln(y²) + 2y = 2x

on differentiating both sides with respect to 'x', we get

`(d(4x^3 + ln(y^2) + 2y))/(dx)= (d(2x))/(dx)`

or

`12x^2+(2)/(y)((dy)/(dx))+2((dy)/(dx))=2`

or

`12x^2+((2)/(y)+2)(dy)/(dx)=2`

or

`((2+2y)/(y))(dy)/(dx)=2-12x^2`

or

`(dy)/(dx)=(y(2-12x^2))/(2+2y)`

or

`(dy)/(dx)=(2y(1-6x^2))/(2(1+y))`

or

`(dy)/(dx)=(y(1-6x^2))/((1+y))`