Question

If f(x) = 4(sin(x))x, find f'(2)?

Answer 1

To find f'(2), we need to find the derivative of f(x) with respect to x using the product rule. Evaluating f'(2) gives us approximately 0.3084.

Step-by-step explanation:

To find f'(2), we need to find the derivative of f(x) with respect to x and evaluate it at x = 2.

Let's start by finding the derivative.

Using the product rule, we have:

f'(x) = (4(sin(x))x)' = (4x)'(sin(x)) + (4(sin(x)))'(x)

f'(x) = 4(sin(x)) + 4x(cos(x))

Now, let's evaluate f'(2).

f'(2) = 4(sin(2)) + 4(2)(cos(2))

Using a calculator, we find that sin(2) ≈ 0.9093 and cos(2) ≈ -0.4161.

Therefore, f'(2) ≈ 4(0.9093) + 4(2)(-0.4161)

f'(2) ≈ 3.6372 - 3.3288

f'(2) ≈ 0.3084