Problem of the Week

Updated at Aug 11, 2025 1:37 PM

How would you differentiate \(\sin{y}+8y\)?

Below is the solution.



\[\frac{d}{dy} \sin{y}+8y\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dy} \sin{y})+(\frac{d}{dy} 8y)\]

2
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[\cos{y}+(\frac{d}{dy} 8y)\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\cos{y}+8\]

Done
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