Question

Evaluate differentiation of x^2 Sin(x) w.r.t Tan(x)Cosec(x)

(a) \(\frac{[2xSin(x)+x^2 Cos(x)]}{-Cosec(x)-Sec^2 (x)Cosec(x)}\)

(b) \(\frac{[2xSin(x)+x^2 Cos(x)]}{-Cosec(x)+Cos(x)Sin(x)}\)

(c) \(\frac{[2xSin(x)+x^2 Cos(x)]}{-Cosec(x)+Sec^2 (x)Cosec(x)}\)

(d) \(\frac{[2xSin(x)+x^2 Cos(x)]}{+Cosec(x)+Sec^2 (x)Cosec(x)}\)

I got this question in an interview for job.

My question is taken from Limits and Derivatives of Several Variables topic in chapter Partial Differentiation of Engineering Mathematics

Answer 1

The correct answer is (c) \(\frac{[2xSin(x)+x^2 Cos(x)]}{-Cosec(x)+Sec^2 (x)Cosec(x)}\)

The explanation is: \(\frac{dx^2 Sin(x)}{dTan(x)Csoec(x)}=\frac{dx^2 Sin(x)}{dx} \frac{dx}{dTan(x)Cosec(x)}\)

\(=\frac{[2xSin(x)+x^2 Cos(x)]}{-Cosec(x)+Sec^2 (x)Cosec(x)}\)