Question

Find differentiation of xSin(x) + ayCos(x) + Tan(y) = 0.

(a) \(\frac{[ayCos(x)-Sin(x)+Cos(x)]}{[aCos(x)+Sec^2 (y)]}\)

(b) \(\frac{[ayCos(x)-Sin(x)+xCos(x)]}{[Cos(x)+Sec^2 (y)]}\)

(c) \(\frac{[ayCos(x)-Sin(x)+xCos(x)]}{[aCos(x)+Sec^2 (y)]}\)

(d) \(\frac{[ayCos(x)-Cos(x)+xCos(x)]}{[aCos(x)+Sec^2 (y)]}\)

I had been asked this question by my school principal while I was bunking the class.

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

Answer 1

Right option is (c) \(\frac{[ayCos(x)-Sin(x)+xCos(x)]}{[aCos(x)+Sec^2 (y)]}\)

The best I can explain: xSin(x) + ayCos(x) + Tan(y) =0

Differentiation of above eqn. is

\(Sin(x) + xCos(x) – ayCos(x) + aCos(x) \frac{dy}{dx} + Sec^2 (y) \frac{dy}{dx}=0\)

\(\frac{dy}{dx}=\frac{[ayCos(x)-Sin(x)+xCos(x)]}{[aCos(x)+Sec^2 (y)]}\)