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Find the derivative of the trigonometric function. f(t) = \frac{\cos t}{t}

Question:

Find the derivative of the trigonometric function.

{eq}f(t) = \frac{\cos t}{t} {/eq}

Answer and Explanation:

Let:

{eq}f(t)=\dfrac{\cos t}{t} {/eq}

We will differentiate the above function using quotient rule for derivatives:

{eq}\dfrac{d}{dx}\left(\dfrac{u}{v}\right)=\dfrac{vu^{'}-uv^{'}}{v^2} \\\begin{align*}f^{'}(t)& =\dfrac{t\dfrac{d}{dt}\cos t-\cos t\dfrac{d}{dt}t}{t^2} \\& =\dfrac{-t\sin t-\cos t}{t^2} \end{align*} {/eq}


Learn more about this topic:

Quotient Rule: Formula & Examples

from Division: Help & Review

Chapter 1 / Lesson 5
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