Question

Consider the following function:

f(x)=4 sin (x)+sin (2 x), [0,2 x]
Find fʹ(x).
fʹ(x)=

Answer 1

To find the derivative of the given function, f(x) = 4sin(x) + sin(2x), over the interval [0, 2x], we can use the chain rule. The derivative is f'(x) = 4cos(x) + 2cos(2x).

Step-by-step explanation:

To find the derivative of the given function, f(x) = 4sin(x) + sin(2x), over the interval [0, 2x], we can use 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, g(x) = 2x, so g'(x) = 2. The derivative of sin(x) is cos(x), and the derivative of sin(2x) is 2cos(2x). Applying the chain rule, we get f'(x) = 4cos(x) + 2cos(2x).