Find f '(x) if f(x) = x⁴ cos x.

Question

Quizplus · Accepted Answer

To find F1F1F1S1F1F1F10(x), we need to apply the differential operator F1F1F1S1F1F1F1 on f(x). Firstly, F1F1F1(f(x)) = x³ sin x (applying the first-order differential operator F1F1F1 to f(x) gives us the derivative of f(x), which is x³ sin x). Next, we apply the differential operator S1 on x³ sin x, which gives us the product of the constant 4 and the original function since S1 multiplies a function by 4 and then subtracts its antiderivative: S1(x³ sin x) = 4x³ cos x - x⁴ sin x. Finally, we apply the differential operator F1F1F10, which gives us the antiderivative of the function obtained in the previous step: F1F1F10(4x³ cos x - x⁴ sin x) = 4x³ cos x - x⁴ sin x + C. Since we are not given any initial or boundary conditions, we cannot determine the constant C, and it can be disregarded. Therefore, the final answer is: F1F1F1S1F1F1F10(x) = 4x³ cos x - x⁴ sin x.

Find F '(X) If F(x) = X4 Cos X

Find F '(X) If F(x) = X⁴ Cos X