Question

Evaluate y^44 + 3xy^3 + 6x^2 y^2 – 7y + 8 = 0.

(a) \(\frac{(7-12x^2 y-9xy^4-4y^3)}{(3y^3+12xy^2)}\)

(b) \(\frac{(7-12x^2 y-9xy^2-4y^3)}{(3y^3+12xy^2)}\)

(c) \(\frac{(7-12x^2 y-9xy^2-4y^3)}{(3y^4+12xy^2)}\)

(d) \(\frac{(7-12x^4 y-9xy^2-4y^3)}{(3y^3+12xy^2)}\)

I got this question in class test.

This interesting question is from Implicit Differentiation topic in section Partial Differentiation of Engineering Mathematics

Answer 1

The correct answer is (b) \(\frac{(7-12x^2 y-9xy^2-4y^3)}{(3y^3+12xy^2)}\)

For explanation: y^44 + 3xy^3 + 6x^2 y^2 – 7y + 8 = 0.

Differentiating it we get

\(4y^3 \frac{dy}{dx}+3[y^3+3xy^2  \frac{dy}{dx}]+6[2xy^2+2x^2 y \frac{dy}{dx}]-7 \frac{dy}{dx}\)=0

\(\frac{dy}{dx}=\frac{(7-12x^2 y-9xy^2-4y^3 )}{(3y^3+12xy^2)}\)