Problem of the Week

Updated at Sep 16, 2024 3:27 PM

How can we find the derivative of \(\cos{z}+3z\)?

Below is the solution.



\[\frac{d}{dz} \cos{z}+3z\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dz} \cos{z})+(\frac{d}{dz} 3z)\]

2
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[-\sin{z}+(\frac{d}{dz} 3z)\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[3-\sin{z}\]

Done
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