consider the following function.
\f(x) = \sin x\
step 5 of 5: find $f^{(37)}(x)$ by observing the pattern of the derivative from the previous steps.
answer 2 points
\f^{(37)}(x) = \

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Trigonometric Derivatives", "Higher-Order Derivatives" ], "new_concepts": [], "current_concepts": [ "Trigonometric Derivatives", "Higher-Order Derivatives" ] } ## Find the first few derivatives of the function $$ \begin{aligned} f(x) &= \sin x \ f'(x) &= \cos x \ f''(x) &= -\sin x \ f'''(x) &= -\cos x \ f^{(4)}(x) &= \sin x \end{aligned} $$ ## Determine the periodic pattern of the derivatives $$ f^{(n)}(x) = f^{(n \pmod 4)}(x) $$ ## Calculate the 37th derivative $$ \begin{aligned} 37 &\equiv 1 \pmod 4 \ f^{(37)}(x) &= f'(x) = \cos x \end{aligned} $$ Consider the following function. $$f(x) = \sin x$$ Step 5 of 5: Find $f^{(37)}(x)$ by observing the pattern of the derivative from the previous steps. $f^{(37)}(x) =$ $\cos x$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Higher-Order Derivatives" ] }

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Question

Explanation:

Find the first few derivatives of the function

Determine the periodic pattern of the derivatives

Calculate the 37th derivative

Answer: