Mathematics 2014 JAMB Past Questions - Question 39: If y=cos 3x,find dy/dx.

Correct Answer

A

Explanation

y = cos 3xLet u = 3x so that y = cos uNow, = - sin uTo find the derivative of y = cos(3x) with respect to x (dy/dx), we can use the chain rule.The chain rule states that if we have a function of the form f(g(x)), the derivative with respect to x is given by f'(g(x)) * g'(x).In this case, g(x) = 3x and f(x) = cos(x).First, let's find the derivative of f(x) = cos(x) with respect to x:f'(x) = -sin(x)Next, let's find the derivative of g(x) = 3x with respect to x:g'(x) = 3Now, we can apply the chain rule to find the derivative of y = cos(3x):dy/dx = f'(g(x)) * g'(x)dy/dx = -sin(3x) * 3dy/dx = -3sin(3x)Therefore, the derivative of y = cos(3x) with respect to x is dy/dx = -3sin(3x).By the chain rule, dy/dx = dy/du x du/dx = (-sin u) (3)= -3 sin u = -3sin3x