Problem of the Week

Updated at Feb 10, 2025 12:04 PM

To get more practice in calculus, we brought you this problem of the week:

How would you differentiate cot⁡t+csc⁡t\cot{t}+\csc{t}?

Check out the solution below!



ddtcot⁡t+csc⁡t\frac{d}{dt} \cot{t}+\csc{t}

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddtcot⁡t)+(ddtcsc⁡t)(\frac{d}{dt} \cot{t})+(\frac{d}{dt} \csc{t})

2
Use Trigonometric Differentiation: the derivative of cot⁡x\cot{x} is −csc⁡2x-\csc^{2}x.
−csc⁡2t+(ddtcsc⁡t)-\csc^{2}t+(\frac{d}{dt} \csc{t})

3
Use Trigonometric Differentiation: the derivative of csc⁡x\csc{x} is −csc⁡xcot⁡x-\csc{x}\cot{x}.
−csc⁡2t−csc⁡tcot⁡t-\csc^{2}t-\csc{t}\cot{t}

Done
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