Question

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

Answer 1

Answer:

$\frac{dy}{dx}=\frac{y(1-6x^2)}{(1+y)}$

Step-by-step explanation:

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

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

$\frac{d(4x^3 + ln(y^2) + 2y)}{dx}= \frac{d(2x)}{dx}$

or

$12x^2+\frac{2}{y}(\frac{dy}{dx})+2(\frac{dy}{dx})=2$

or

$12x^2+(\frac{2}{y}+2)\frac{dy}{dx}=2$

or

$(\frac{2+2y}{y})\frac{dy}{dx}=2-12x^2$

or

$\frac{dy}{dx}=\frac{y(2-12x^2)}{2+2y}$

or

$\frac{dy}{dx}=\frac{2y(1-6x^2)}{2(1+y)}$

or

$\frac{dy}{dx}=\frac{y(1-6x^2)}{(1+y)}$