Question

If z = e^x Sin(Cos(x))Cos(Sin(x)) Then find ^dz⁄dx

(a) [e^xSin(Cos(x))Cos(Sin(x))-e^xCos(x)Cos(Cos(x))Cos(Sin(x))-e^xSin(x)Sin(Cos(x))Sin(Sin(x))]

(b) [e^xSin(Cos(x))Cos(Sin(x))-e^xSin(x)Cos(Cos(x))Cos(Sin(x))-e^xCos(x)Sin(Cos(x))Sin(Sin(x))]

(c) [e^xCos(Cos(x))Sin(Sin(x))-e^xSin(x)Cos(Cos(x))Cos(Sin(x))-e^xCos(x)Sin(Cos(x))Sin(Sin(x))]

(d) [e^xSin(Cos(x))Cos(Sin(x))-e^xCos(x)Cos(Cos(x))Cos(Sin(x))-e^xSin(x)Sin(Cos(x))Sin(Sin(x))]

This question was posed to me during an interview.

Origin of the question is Limits and Derivatives of Several Variables in chapter Partial Differentiation of Engineering Mathematics

Answer 1

Correct choice is (b) [e^xSin(Cos(x))Cos(Sin(x))-e^xSin(x)Cos(Cos(x))Cos(Sin(x))-e^xCos(x)Sin(Cos(x))Sin(Sin(x))]

Best explanation: ^dz⁄dx = ^d⁄dx e^x Sin(Cos(x))Cos(Sin(x)) = [(e^x Sin(Cos(x))Cos(Sin(x)) – e^x Sin(x)Cos(Cos(x))Cos(Sin(x)) – e^x Cos(x)Sin(Cos(x))Sin(Sin(x)))].