Answer
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Step 1:I'll solve this derivative problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Recall the derivative rule for sine function
The derivative of $$\sin(x)$$ is $$\cos(x)$$.
However, we have a negative sign in front of \sin(x), which will affect the derivative.
Step 3:: Apply the chain rule and constant multiple rule
\frac{d}{dx}[-\sin(x)] = -\frac{d}{dx}[\sin(x)]
Step 4:: Compute the derivative
-\frac{d}{dx}[\sin(x)] = -\cos(x)
Final Answer
Key Insights: - The negative sign "comes along" when differentiating - The derivative of \sin(x) is \cos(x) - Multiplying by - 1 gives us -\cos(x)
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