Question Detail
Question
Given that y = x/(2x+5). Find dy/dx
Correct Answer
Option D is the correct answer.
Detailed Explanation
To find dy/dx for y = x/(2x+5), use the quotient rule for differentiation: d/dx(u/v) = (u'v - uv')/v².Let u = x, so u' = d/dx(x) = 1.Let v = 2x+5, so v' = d/dx(2x+5) = 2.Apply the quotient rule:dy/dx = ( (1)(2x+5) - (x)(2) ) / (2x+5)²dy/dx = ( 2x+5 - 2x ) / (2x+5)²dy/dx = 5 / (2x+5)².This matches option D.
Hint
Apply the quotient rule for differentiation. Identify the numerator and denominator functions, find their derivatives, and then substitute into the formula.