Final answer:
The question asks for the derivative of y=sin x+2x^cos x using log differentiation. Logarithmic properties, implicit differentiation, the product rule, and the chain rule are used to find the derivative dy/dx.
Step-by-step explanation:
The student asks for assistance with finding the derivative of y = sin x + 2xcos x using log differentiation. To accomplish this, apply the natural logarithm to both sides of the equation, obtaining ln(y) = ln(sin x + 2xcos x). Then differentiate both sides with respect to x, using implicit differentiation for the left side, which becomes (1/y)(dy/dx), and applying the product rule, chain rule, and properties of logarithms for the right side. After differentiating, solve for dy/dx by multiplying through by y, which in terms of x is the original function sin x + 2xcos x.