Question

Find a formula for $\frac{dy}{dx}$ for the implicit function $ax^2 + xy^2 + b\ln y = c$. The constants $a$, $b$, and $c$ may appear in your answer. $\frac{dy}{dx} = \frac{-2ax - y^2}{2xy + \frac{b}{y}}$ DNE $\frac{dy}{dx} = 2x^2 + 2xy + \frac{b}{y} + c$ $\frac{dy}{dx} = \frac{2x - ay}{2xb - y}$

          Find a formula for $\frac{dy}{dx}$ for the implicit function $ax^2 + xy^2 + b\ln y = c$. The constants $a$, $b$, and $c$ may appear in your answer.
$\frac{dy}{dx} = \frac{-2ax - y^2}{2xy + \frac{b}{y}}$
DNE
$\frac{dy}{dx} = 2x^2 + 2xy + \frac{b}{y} + c$
$\frac{dy}{dx} = \frac{2x - ay}{2xb - y}$

Find a formula for (dy)/(dx) for the implicit function ax^2 + xy^2 + bln y = c. The constants a, b, and c may appear in your answer.
(dy)/(dx) = (-2ax - y^2)/(2xy + (b)/(y))
DNE
(dy)/(dx) = 2x^2 + 2xy + (b)/(y) + c
(dy)/(dx) = (2x - ay)/(2xb - y)

Added by Virginia C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/02/2022

Step 1

We have: d/dx (ax^2 + xy^2 + b*ln(y)) = d/dx (c) 2ax + y^2(dy/dx) + 2xy(dy/dx) + b/y(dy/dx) = 0 Show more…

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Find a formula for (dy)/(dx) for the implicit function ax^(2)+xy^(2)+b*ln(y)=c. The constants a, b, and c may appear in your answer. (dy)/(dx)=(-2ax-y^(2))/(2xy+(b)/(y)) DNE (dy)/(dx)=2x^(2)+2xy+(b)/(y)+c (dy)/(dx)=(2x-ay)/(2xb-y) Find a formula for dy/dx for the implicit function ax^(2)+xy^(2)+b*ln(y)=c. The constants a, b, and c may appear in your answer. DNE dy/dx =2x+2xy+c/y dy/dx 2x-ay 2xb-y