find the derivative of the following function.\ny = 3 sin x + 8 cos x\n\\frac{dy}{dx}=\\square
find the derivative of the following function.\ny = 3 sin x + 8 cos x\n\\frac{dy}{dx}=\\square
Answer
Explanation:
Step1: Differentiate (3\sin x)
The derivative of (\sin x) is (\cos x). Using the constant - multiple rule ((cf(x))^\prime = cf^\prime(x)), for (y_1 = 3\sin x), we have (y_1^\prime=3\cos x).
Step2: Differentiate (8\cos x)
The derivative of (\cos x) is (-\sin x). Using the constant - multiple rule ((cf(x))^\prime = cf^\prime(x)), for (y_2 = 8\cos x), we have (y_2^\prime=- 8\sin x).
Step3: Use the sum rule
If (y = y_1 + y_2), then (y^\prime=y_1^\prime + y_2^\prime). Substituting (y_1^\prime) and (y_2^\prime) into the sum rule formula, we get (\frac{dy}{dx}=3\cos x-8\sin x).
Answer:
(3\cos x - 8\sin x)