Mathematics 2002 JAMB Past Questions - Question 8: find the derivative of y = sin²(5x) with respect to x

Correct Answer

A

Explanation

To find the derivative of y = sin²(5x) with respect to x, we can use the chain rule.Let's start by rewriting the expression using the power rule for differentiation:y = (sin(5x))^2Now, let's apply the chain rule. The chain rule states that if we have a composite function f(g(x)), the derivative is given by f'(g(x)) * g'(x).In this case, f(u) = u^2 and g(x) = sin(5x).First, let's find the derivative of f(u) = u^2 with respect to u:f'(u) = 2uNext, let's find the derivative of g(x) = sin(5x) with respect to x:g'(x) = 5 * cos(5x)Now, we can apply the chain rule:dy/dx = f'(g(x)) * g'(x)dy/dx = 2 * (sin(5x))^1 * 5 * cos(5x)Simplifying:dy/dx = 10 * sin(5x) * cos(5x)Therefore, the derivative of y = sin²(5x) with respect to x is dy/dx = 10 * sin(5x) * cos(5x).