Question

Value of \(\frac{dSin(x)Cos(x)}{dx}\) is

(a) Cos(2x)

(b) Sin(2x)

(c) Cos^2(2x)

(d) Sin^2(2x)

I have been asked this question by my college professor while I was bunking the class.

My enquiry is from Limits and Derivatives of Several Variables topic in portion Partial Differentiation of Engineering Mathematics

Answer 1

Right choice is (a) Cos(2x)

The explanation: \(\frac{dSin(x)Cos(x)}{dx} = Cos(x) \frac{dSin(x)}{dx} + Sin(x) \frac{dCos(x)}{dx}\) = Cos^2(x) – Sin^2(x) = Cos(2x).