Question

Find the derivative of Tan(x) = Tan(y).

(a) \(\frac{1+x^2}{1+y^2}\)

(b) \(\frac{1+y}{1+x^2}\)

(c) \(\frac{1+y^2}{1+x^2}\)

(d) \(\frac{1+y^2}{1+x}\)

The question was asked in exam.

This question is from Implicit Differentiation in portion Partial Differentiation of Engineering Mathematics

Answer 1

Right choice is (c) \(\frac{1+y^2}{1+x^2}\)

To explain: Tan(y)=Tan(x)

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

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