Mathematics 2007 JAMB Past Questions - Question 15: If y = (1 + x)² , find dy/dx

Correct Answer

C

Explanation

If y = (1+x)sup2, find dy /dx, y = (1+x)sup2dy /dx = 2 (1+x) 1=2+2xTo find the derivative of y = (1 + x)² with respect to x, we can use the power rule of differentiation.The power rule states that if we have a function of the form f(x) = (g(x))^n, where g(x) is a differentiable function and n is a constant, then the derivative is given by:d/dx [f(x)] = n * (g(x))^(n-1) * g'(x)In this case, g(x) = 1 + x and n = 2.Taking the derivative:dy/dx = 2 * (1 + x)^(2-1) * (1 + x)'The derivative of (1 + x) with respect to x is simply 1.Simplifying:dy/dx = 2 * (1 + x) * 1      = 2(1 + x)Therefore, the derivative of y = (1 + x)² with respect to x is dy/dx = 2(1 + x).