Mathematics 2015 JAMB Past Questions - Question 13: If y=3sin(-4x),dy/dx is

Correct Answer

D

Explanation

y=3sin(-4x)dy/dx=-12cos(-4x)To find the derivative of y = 3sin(-4x) with respect to x, we can use the chain rule of differentiation. The chain rule states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x), where f'(g(x)) is the derivative of the outer function evaluated at the inner function, and g'(x) is the derivative of the inner function.In this case, the outer function is sin(u), where u = -4x, and the inner function is -4x.The derivative of sin(u) with respect to u is cos(u), and the derivative of -4x with respect to x is -4.Using the chain rule, we can find dy/dx as follows:dy/dx = 3 * cos(-4x) * (-4)    = -12cos(4x)Therefore, the derivative of y = 3sin(-4x) with respect to x is dy/dx = -12cos(4x).