College Math Placement Practice Test

Question: 1 / 400

What is the derivative of f(x) = sin(x)?

sin(x)

cos(x)

The derivative of the function \( f(x) = \sin(x) \) is determined using the fundamental rules of differentiation in calculus. Specifically, it is known that the derivative of the sine function is the cosine function. This relationship comes from the limit definitions and the fundamental properties of trigonometric functions.

When differentiating \( \sin(x) \) with respect to \( x \), you arrive at \( \cos(x) \). This reflects how the slope of the sine curve varies as \( x \) changes. At any point on the sine curve, the rate of change (or slope) is equal to the value of the cosine function at that point.

Thus, for this particular question, the derivative of \( f(x) = \sin(x) \) confirms that the correct answer is indeed the cosine function, \( \cos(x) \).

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-sin(x)

-cos(x)

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