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This requires logarithmic differentiation. Take the natural logarithm of both sides: ln(y) = ln(xtan x). Using logarithm properties, ln(y) = tan(x) * ln(x). Now differentiate both sides with respect to x using implicit differentiation and the product rule:(1/y) * dy/dx = (d/dx [tan x]) * ln(x) + tan(x) * (d/dx [ln x])(1/y) * dy/dx = sec2(x) * ln(x) + tan(x) * (1/x)Multiply both sides by y: dy/dx = y * (sec2(x) * ln(x) + tan(x)/x).Substitute y = xtan x back: dy/dx = xtan x * (sec2(x) * ln(x) + tan(x)/x). Rearranging the terms inside the parenthesis to match the option: dy/dx = xtan x * (tan(x)/x + sec2(x) * ln(x)).