Question Detail
Question
Given that y = x/(2x+5). Find dy/dx
Correct Answer
Option D is the correct answer.
Detailed Explanation
To find the derivative of y = x/(2x+5), we use the quotient rule for differentiation, which states: d/dx (u/v) = (u'v - uv')/v².Let u = x, then u' = d/dx(x) = 1.Let v = 2x+5, then v' = d/dx(2x+5) = 2.Substitute u, u', v, and v' into the quotient rule formula:dy/dx = (1 * (2x+5) - x * 2)/(2x+5)²Simplify the numerator:= (2x+5 - 2x)/(2x+5)²= 5/(2x+5)². This matches option D.
Hint
Apply the quotient rule for differentiation: d/dx (u/v) = (u'v - uv') / v², where u is the numerator and v is the denominator.