Find $\frac{d y}{d x}$ for the following function
\[
y=6 \sin x+9 \cos x
\]

Answer

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Answer

Final Answer: The derivative of the function $y=6 \sin x+9 \cos x$ is $\boxed{-9 \sin x+6 \cos x}$.

Steps

Step 1 ：Given the function $y=6 \sin x+9 \cos x$.

Step 2 ：We need to find the derivative of the function.

Step 3 ：The derivative of $\sin x$ is $\cos x$ and the derivative of $\cos x$ is $-\sin x$.

Step 4 ：Applying these rules to the given function, we get $\frac{d y}{d x} = -9\sin x + 6\cos x$.

Step 5 ：Final Answer: The derivative of the function $y=6 \sin x+9 \cos x$ is $\boxed{-9 \sin x+6 \cos x}$.